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In a right triangle the ratio of the length of the side opposite an acute angle to the length of the hypotenuse?
Wiki User
∙ 15y ago
sin θ : 1 = the length of opposite side to angle θ : the length of the hypotenuse
Wiki User
∙ 15y ago
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How do you determine which is the adjacent side of a right triangle?
There are three sides, hypotenuse, opposite and adjacent. But the adjacent and opposite are not fixed sides: it depends on which of the two acute angles you are examining.For either of the non-right angles, the adjacent side is the one which forms the angle, along with the hypotenuse. For the given angle θ, the length of the adjacent side compared to the hypotenuse (adjacent/hypotenuse) is the cosine (cos θ).
How do you find the short leg of a right triangle?
The answer depends on what information you do have about the triangle: the lengths of the other two sides, or the hypotenuse (longest side) and one of the acute angles, or the other leg and one of the acute angles, etc.
A hypotenuse and an acute angle define congruence?
Yes. If you know two angles of a triangle, then you know all three. Why? Because they sum to 180 deg. So you have the hypotenuse and the angles at either end then you have ASA. AAS may not be sufficient for congruence but ASA IS. Another way of looking at it: suppose the hypotenuse is h and the known acute angle is x. Then, the side adjacent to the angle is h*cos(x) while the side opposite is h*sin(x). So the two hypotenuses are of length h, the two sides adjacent to the known acute angle are h*cos(x) each and the sides opposite are h*sin(x). And all three pairs of angles are equal. What else do you need to show congruence?
In A Triangle The Smallest Angle Is?
In a triangle the smallest angle is always opposite the shortest side. It will always be an acute angle.
Name all types of triangles for which the point of concurrency is inside the triangle?
The answer depends on what point of concurrency you are referring to. There are four segments you could be talking about in triangles. They intersect in different places in different triangles. Medians--segments from a vertex to the midpoint of the opposite side. In acute, right and obtuse triangles, the point of concurrency of the medians (centroid) is inside the triangle. Altitudes--perpendicular segments from a vertex to a line containing the opposite side. In an acute triangle, the point of concurrency of the altitudes (orthocenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Perpendicular bisectors of sides--segments perpendicular to each side of the triangle that bisect each side. In an acute triangle, the point of concurrency of the perpendicular bisectors (circumcenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Angle bisectors--segments from a vertex to the opposite side that bisect the angles at the vertices. In acute, right and obtuse triangles, the point of concurrency of the angle bisectors (incenter) is inside the triangle.
What is sine in trigonometry?
The sine of one of the acute angles in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
The hypotenuse of a right triangle is the opposite side acute?
Angles are acute, not sides.
Is the hypotenuse always opposite an acute angle?
The hypotenuse is NEVER opposite an acute angle. It's always the side of the right triangle that's opposite the right angle.
How do you find the angle of a right triangle with the length of two legs?
-- Like every triangle, a right triangle has three interior angles.-- Unlike any other triangle, one of the angles in a right triangle is a right angle.The other two are both acute angles.-- One acute angle is the angle whose cosine is length of one leg / length of hypotenuse-- Other acute angle is the angle whose sine is length of the same leg / length of the hypotenuse-- The length of the hypotenuse is the square root of [ (length of one leg)2 + length of other leg)2 ]
How do you determine which is the adjacent side of a right triangle?
There are three sides, hypotenuse, opposite and adjacent. But the adjacent and opposite are not fixed sides: it depends on which of the two acute angles you are examining.For either of the non-right angles, the adjacent side is the one which forms the angle, along with the hypotenuse. For the given angle θ, the length of the adjacent side compared to the hypotenuse (adjacent/hypotenuse) is the cosine (cos θ).
How do you find the hypotenuse with only a leg and a degree?
If it's a right angle triangle and an acute angle plus the length of a leg is given then use trigonometry to find the hypotenuse.
Which angle has hypotenuse?
For a right angle triangle its hypotenuse is opposite its angle of 90 degrees and its other two angles are acute and its 3 angles add up to 180 degrees.
What is the sin of angle a in a right triangle?
The sine of an acute angle in a right triangle is equal to the ratio (length of opposite side)/(length of hypotenuse). The hypotenuse of a right triangle is the longest side, and is opposite of the right angle.This may help you remember it:Sin Cos TanO H A H O A. O means Opposite. A means Adjacent, and H means Hypotenuse.Oh Heck Another Hour Of Algebra.So Sin(Θ) = O/H ; Cos(Θ) = A/H ; and Tan(Θ) = O/A
What is the hypotenuse angle theorem?
The hypotenuse angle theorem, also known as the HA theorem, states that 'if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.'
What are the dimensions and area of a right angle triangle whose hypotenuse is 8.75 cm?
The length of the hypotenuse is not sufficient information. You need the length of one of the legs or one of the acute angles. Or some other information that will enable you to derive that.
How do you find the legs of a right triangle if you know the hypotenuse?
If that's all you know, then you can't. Whatever the length of the hypotenuse is, there arean infinite number of right triangles that all have the same length hypotenuse.In order to define one unique right triangle, you need to know one of the following in addition tothe length of the hypotenuse:-- the length of one leg-- the size of either acute angle
How do you find the base and the height of a triangle if you have the hypotenuse?
You cannot. You need to know the length of one of the sides to find the other, or either of the acute angles.
