In triangle ABC, angle C is 90 degrees, AC = 16, sinA = 8/17. Find BC. the response should be 30.

Given:

ABC – right-angled triangle;

Angle C = 90 degrees;

AC = 16;

sin A = 8/17;

Find BC.

Solution:

1) In order to find the BC of the triangle ABC, we use the formula:

sin A = BC / AB and cos a = AC / AB;

From here we get:

AB = BC / sin a;

AB = AC / cos a;

Since AB = AB, we get an expression in the form:

ВС / sin a = AC / cos a;

BC = AC * sin a / cos a;

Hence, AB = AC / cos a;

All values except cos a are known.

2) Find cos a

cos a = √ (1 – sin ^ 2 a) = √ (1 – (8/17) ^ 2) = √ (289 – 64) / 17 = 5/17;

3) Calculate BC.

BC = AC * sin a / cos a = 16 * 8/17 / (5/17) = 16 * 8/17 * 17/5 = 16 * 8/5 = 25.6.

Answer: BC = 25.6.