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When the vertex angle and the base of an isosceles triangle are given how do you find its area?
Wiki User
∙ 10y ago
Let's A and x represent the given vertex angle and the base, respectively.
Use the law of cosine to find the length of the legs of the triangle by doing x2 = m2 + n2 - 2mncos A, where m and n are the legs. Since the triangle is isosceles, m = n and therefore x2 = 2m2 - 2m2cos A. Solving for m gives m = sqrt(x2/(2 - cos A))
Get the height of the triangle by using Pythagorean theorem. m2 = x2 + h2, where h is the height.
Finally, get the area using the formula for a triangle's area, which is (base * height) / 2.
Wiki User
∙ 10y ago
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Could a triangle with sides 8cm 6cm 8cm long be a scalene triangle?
No because the dimensions given relate to an isosceles triangle.
How would you construct an isosceles triangle if only given the altitude to the base and a base angle?
Start with the altitude (height) and draw that. Draw the actual length of the altitude on your paper, or draw it to scale. Naturally you'll draw it down the middle of your paper parallel to the sides (perpendicular to the bottom) of your paper. Now that you have your altitude, draw a line perpendicular to it across the bottom. Your base will be on that, but we don't know how big it is yet. Let's work with your base angle, but indirectly. You have a vertical line perpendicular to another line. There are two right angles formed, one on each side of the vertical line. If you could draw in one side of your isosceles triangle, you'd have a right triangle that represents half your isosceles triangle. The altitude divides your isosceles triangle exactly in half down the middle. This right triangle will, like all triangles, have interior angles that add up (sum) to 180 degrees. Now we use the base angle. You have the 90 degree angle, and the base angle. That base angle and the "top" angle will add up to 90 degrees, and that's so that these two angles and the 90 angle where the altitude meets the base will add up to 180 degrees. That means the base angle and the top angle will have to add up to 90 degrees. Subtract your base angle from 90 degrees and you'll have your "top" angle. Get you protractor, place it at the top of your altitude, and mark the "top" angle. Now draw a line from the top of the altitude on this angle you set, and continue it to the base. That's one side of your triangle. Repeat this on the other side and your isosceles triangle will appear.
How many triangles exist with the given side lengths 4m 4m 7m?
A triangle with two equal sides is an isosceles triangle and you can have as many as you like.
What Two angle measures of this triangle are 60 and deg. Which type of triangle is it?
An equilateral triangle would fit the given description
What are secondary parts of a triangle in geometry?
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC.the secondary parts are at the bottom.the secondary parts of the trianglemedian - a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite sideangle bisector - a segment which bisects an angle and whose endpoints are a vertex of the triangle and a point on the opposite sidealtitude - a segment from the vertex of the triangle perpendicular to the line containing the opposite sideperpendicular bisector - a line whose points are equidistant from the endpoints of the given side.incenter - the point of concurrency of the three angle bisectors of the trianglecentroid - the point of concurrency of the three medians of the triangleorthocenter - the point of concurrency of the three altitudes of the trianglecircumcenter - the point of concurrency of the three perpendicular bisectors of the sides of the triangle .by merivic lacaya and acefg123ZNNHS Student. Toronto university student
How would you construct an isosceles triangle if only given the vertex angle and the radius of the circumscribed circle?
You have an isosceles triangle, and a circle that is drawn around it. You know the vertex angle of the isosceles triangle, and you know the radius of the circle. If you use a compass and draw the circle according to its radius, you can begin your construction. First, draw a bisecting cord vertically down the middle. This bisects the circle, and it will also bisect your isosceles triangle. At the top of this cord will be the vertex of your isosceles triangle. Now is the time to work with the angle of the vertex. Take the given angle and divide it in two. Then take that resulting angle and, using your protractor, mark the angle from the point at the top of the cord you drew. Then draw in a line segment from the "vertex point" and extend it until it intersects the circle. This new cord represents one side of the isosceles triangle you wished to construct. Repeat the process on the other side of the vertical line you bisected the circle with. Lastly, draw in a line segment between the points where the two sides of your triangle intersect the circle, and that will be the base of your isosceles triangle.
How do you construct an isosceles triangle when base and angle at the vertex is given?
First find 180 minus the vertex angle and divide that by 2 to get the other angles. Then solve the other sides by using sin(vertex angle)/base=sin(other angles)/other sides.
What is The sum of any 2 sides of an isosceles triangle?
Depends from the given information. For example, if it is given the measure of the angle base θ, and the length of the base b, the sum of the sides a of the isosceles triangle equals to 2a = b/cos θ If it is given the measure of the angle base θ, and the length of the height h, the sum of the sides a of the isosceles triangle equals to 2a = 2h/sin θ If it is given the measure of the vertex angle θ, and the length of the base b, the sum of the sides a of the isosceles triangle equals to 2a = b/sin θ/2 If it is given the measure of the vertex angle θ, and the length of the height h, the sum of the sides a of the isosceles triangle equals to 2a = 2h/cos θ/2 If it is given the length measures of the base b and the height h, the sum of the sides a of the isosceles triangle equals to 2a = √(h4 + b2) (from the Pythagorean theorem)
What is the measure of each base angle of an isosceles triangle if the vertex measures 6X plus 8 and 9X-25?
If the two expressions given for the vertex angle are to be the same number, 6x + 8 = 9x -25; then 3x = 25 + 8 = 33 and x = 11. Therefore, the vertex angle is 6(11) + 8 = 74. The two base angles of an isosceles triangle must be the same and the three angles of the triangle must sum to 180. Therefore, calling the unknown base angle y, 2y + 74 = 180, or y equals 53.
What is the measurement of the 3rd angle for a triangle given both angle measurement 54 degrees?
It is an isosceles triangle and the 3rd angle is 72 degrees.
What is the deffinition of a 45-45-90 triangle?
It is an isosceles right angle triangle if the given numbers are in degrees
Can the area of a triangle be found when only one specified length is given?
Yes providing that it's an equilateral triangle or a right angle isosceles triangle.
How do you find the lengths of the legs of an isoceles triangle when given the angle?
With only the angle provided, you cannot find the lengths of the sides. The reason for this is that the isosceles triangle can be scaled up or down. If you had an isosceles triangle with a vertex of, say, 20 degrees, the other two angles would be 80 degrees each. This triangle could be constructed with the pair of congruent sides 10 centimeters long, 10 feet long, 10 miles long, or any length, and it would still have the same angles in its construction. Angles alone are insufficient to discover the length of the sides of an isosceles triangle.
How do i prove if the base angles of a triangle are congruent then the triangle is isosceles?
Suppose you have triangle ABC with base BC, and angle B = angle C. Draw the altitude AD.Considers triangles ABD and ACDangle ABD = angle ACD (given)angle ADB = 90 deg = angle ACDtherefore angle BAD = angle CADAlso the side AD is common to the two triangles.Therefore triangle ABD is congruent to triangle ACD (ASA) and so AB = AC.That is, triangle ABC is isosceles.
What is the measure of each angle of an isosceles triangle?
We have no way to know that, from the information given in the question. All we know, if the triangle is isosceles, is that two of the angles are equal, and that all three angles sum to 180 degrees.
What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 70 degrees and its congruent sides each measure 15 cm?
When finding the angles, the length of the sides is irrelevant in this case.Let the triangle be ABC with ∠A the vertex and BC the base; the real question is whether you have the isosceles triangle "drawn" and labelled with the equal sides:either side of the "vertex" making the equal angles ∠B and ∠CThe equal sides are AB and AC; the base being the odd length means the angles at each end of it are the same, thus: vertex_angle = 180o - 2 x 70o= 40othe base and one side to the vertex equal (say sides AB and BC) and the other side different (AC) making the equal angles ∠A and ∠C70o angle is between the sides of equal length (∠B):The vertex is one of the two equal angles: vertex_angle = (180o - 70o) ÷ 2= 55o70o angle is between the odd side and the base (∠C):The vertex angle (∠A) is the same as the given angle (∠C), that is 70o Isosceles triangles are often drawn in the first case, but it is not necessarily so!
When the vertex angle and the base of an isosceles triangle are given how do you find its perimeter?
Using the trigonometry ratio for the cosine and by halving the base lenght which will result in two right angled triangles. Then after working out the hypotenuse simply double it and add on the original base length.
