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In right triangle ABC with angle C = 90, angle B = 75, and side AB = 12 cm. Find area

User Daylene
by
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1 Answer

4 votes

Answer:

about 18 cm^2

Explanation:

The formula for the area of a right triangle is A = ab/2 where a is the side opposite angle A and b is the side opposite angle B. We need to figure out what a and b are.

Use sine relationship to figure out b:

(Note: c is the side opposite angle C)

sin75 = b/c = b/12cm

b = 12 cm x sin 75 = 11.59 cm

Use cosine relationship to figure out a:

cos75 = a/c = a/12cm

a = 12 cm x cos 75 = 3.106 cm

Plug into Area formula:

A = (11.59 cm x 3.106 cm) / 2 = 18.0 cm^2

User Darlene
by
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