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What is relationship between exterior angles and opposite interior angles of a triangle?
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. So if a triangle had points A, B and C: The exterior angle at B would equal the sum of interior angles at A and C. Similarly, the exterior angle at C would equal the sum of interior angles at A and B And the the exterior angle at A would equal the sum of interior angles at C and B.
Is the compliment of an acute angle an acute angle?
Yes, since a+b=90, a and b being the two angles, and an acute angle is less than ninety, it is impossible for an angle to be greater or equal to ninety. Thats why.
What is sine equation?
the sine rule, angle (a) and opposite length is eaqual to angle (b) and opposite length. which are also equal to angle (c) and opposite length. Sin A = Sin B = Sin C ------- -------- ---------- a -------- b -------- c
Why is it impossible to have an obtuse equilateral triangle?
This is not a formal proof, but should sufficiently show how to go about proving it.In a triangle, there can be no more than one obtuse angle, because the sum of the angles equal 180°. If angle A is obtuse (greater than 90°), then the sum of the other two angles (B + C) must be less than 90°, so each angle B & C must be less than 90°.An equilateral triangle has 3 equal sides. From the Law of Sines, the sines of the angles (opposite a side) are in the same proportion as the proportions of the lengths of sides.Example: if angle A is opposite side a, and angle B is opposite side b. then:a : b = sinA : sinB, or rearranging: a/sinA = b/sinB.Since the triangle is equilateral, then a = b, and sinA = sinB. Let's assume we can get an equilateral triangle which has one obtuse angle. So assume angle A is obtuse. Angle B does not have to equal angle A, because there are two angles which have the same sine: sin(A) = sin(180°-A). Since A is obtuse, neither B or C can be obtuse (from the first paragraph), so angle B cannot equal A, so it must equal (180°-A).Let's find angle C: Sum up the angles: A + B + C = 180°. Substitute (180°-A) for B: A + (180°-A) + C = 180°, so we find that angle C = 0°, and it is not a triangle. But let's go on. We know that, since it's equilateral, then side c equals a & b, so sin(C) must equal sin(A) and sin(B). Since A is obtuse, then B & C cannot be obtuse, so angles B & C are equal, which means that angle B is also 0°, and angle A must be 180° to satisfy the sum of the angles equal 180°. So we now have a straight line, and the Law of Sines doesn't hold anymore since we have 0 : 0 : 0 {Sin(180°) : Sin(0°) : Sin(0°)}, and you cannot have a ratio with all zeros and be meaningful.
What is B if A is equal to 10 and C the hypotenuse of the triangle is 14.5 not sure how to do this?
If it is a right angle triangle then use Pythagoras' theorem and it works out that B is equal to 10.5 units
