Question

Solve the right triangle.

Round your answers to the nearest tenth.
Check
20
a
B = 48°
-0
0 =
C =
X

Answer 1

∠ B = 48° , a ≈ 18.0 , c ≈ 26.9

Explanation:

∠ B = 180° - ( 90 + 42)° = 180° - 132° = 48°

using the tangent ratio in the right triangle

tan42° =
`(opposite)/(adjacent)` =
`(a)/(20)` ( multiply both sides by 20 )

20 × tan42° = a , then

a ≈ 18.0 ( to the nearest tenth )

using the cosine ratio in the right triangle

cos42° =
`(20)/(c)` ( multiply both sides by c )

c × cos42° = 20 ( divide both sides by cos42° )

c =
`(20)/(cos42)` ≈ 26.9 ( to the nearest tenth )