Question

Question 5 1:47:3 In the obtuse triangle ABC, B = 23, AB = 20 in., and BC| = 30 in.. The length of the height from the point B is: A 1 14,77 in. -B 15,77 in. क С 16,77 in.​

Answer 1

In the obtuse triangle ABC, B = 23, AB = 20 in., and BC| = 30 in.. The length of the height from the point B is: A 1 14,77 in. -B 15,77 in. क С 16,77 in.

Answer 2

The length of height from vertex B to base AC is (C) 16.77 inches

Given:  ∠B = 23°, AB = 20 inches , and BC = 30 inches

To Find: The length of the height from the point B

Solution:

According to the cosine rule,

b² = a² + c² - 2ac cos B

b² = 20² + 30² - 2×20×30 cos 23°

b = √(1300 - 1200 cos 23°)

[ABC] = 1/2 × 20 × 30 sin 23°

          = 300 sin 23°

Now let's assume that the altitude from B meets the extended part of AC at D

So the length of height from vertex B to base AC is;

BD = 2 × 300 sin 23° / √(1300 - 1200 cos 23°)

     ≅ 16.77 inches

Hence, the length of height from vertex B to base AC is (C) 16.77 inches

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