Question

Need help solving triangle in picture

Answer 1

see explanation

Explanation:

Using the sine ration on the left, right triangle

sin35° =
`(opposite)/(hypotenuse)` =
`(a)/(8.6)` ( multiply both sides by 8.6 )

8.6 × sin35° = a , thus

a ≈ 4.93 cm

a + b = 15.7, so

4.93 + b = 15.7 ( subtract 4.93 from both sides )

b = 10.77

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Using the cosine ratio on the left, right triangle

cos35° =
`(adjacent)/(hypotenuse)` =
`(y)/(8.6)` ( multiply both sides by 8.6 )

8.6 × cos35° = y , so

y ≈ 7.04 cm

Using Pythagoras' identity on the right, right triangle

c² = b² + y² = (10.77)² + (7.04)² = 115.99 + 49.56 = 165.55

Take the square root of both sides )

c =
`√(165.55)` ≈ 12.87 cm