Question

What are the exact side lengths of the triangle shown? Leave in radical form

Answer 1

b = 4
`√(3)` , c = 8

Explanation:

using the tangent and cosine ratios in the right triangle and the exact values

tan60° =
`√(3)` , cos60° =
`(1)/(2)` , then

tan60° =
`(opposite)/(adjacent )` =
`(b)/(4)` =
`√(3)` ( multiply both sides by 4 )

b = 4
`√(3)`

then

cos60° =
`(adjacent)/(hypotenuse)` =
`(4)/(c)` =
`(1)/(2)` ( cross- multiply )

c = 4 × 2 = 8