Question

Solving a right triangle ‼️ (Round to the nearest tenth) Can someone help me find B,a, and c ❓

Answer 1

see explanation

Explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles from 180° for B

B = 180° - (90 + 47)° = 180° - 137° = 43°

Use the tangent and cosine ratios in the right triangle for a and c

tan47° =
`(opposite)/(adjacent)` =
`(a)/(18)`

Multiply both sides by 18

18 × tan47° = a , thus

a ≈ 19.3 ( to the nearest tenth )

cos47° =
`(adjacent)/(hypotenuse)` =
`(18)/(c)`

Multiply both sides by c

c × cos47° = 18 ( divide both sides by cos47° )

c =
`(18)/(cos47)` ≈ 26.4 ( to the nearest tenth )