Question

Find x
a) 21 √2
b)7
c)21 √2/2
d)21 √3/2

Answer 1

C

Explanation:

Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values

sin60° =
`(√(3) )/(2)` , cos45° =
`(1)/(√(2) )` , thus

sin60° =
`(opposite)/(hypotenuse)` =
`(opp)/(7√(3) )` =
`(√(3) )/(2)` ( cross- multiply )

2 × opp = 21 ( divide both sides by 2 )

opp =
`(21)/(2)`

Now consider the right triangle on the right, using the cosine ratio

cos45° =
`(adjacent)/(hypotenuse)` =
`((21)/(2) )/(x)` =
`(1)/(√(2) )` ( cross- multiply )

x =
`(21)/(2)` ×
`√(2)` =
`(21√(2) )/(2)` → C