Question

Find x. A. 21√2 B. 7 C. 21√3 over 2 D. 21√2 over 2

Answer 1

D

Explanation:

Using sine ratio in left right angled triangle to find the altitude a of the large triangle which is common to both right triangles and the exact value

sin60° =
`(√(3) )/(2)` , then

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

2a = 21 ( divide both sides by 2 )

a =
`(21)/(2)`

Using the cosine ratio in the right side triangle and the exact value

cos45° =
`(1)/(√(2) )` , then

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

x =
`√(2)` a =
`√(2)` ×
`(21)/(2)` =
`(21√(2) )/(2)` → D

Answer 2

D

Explanation:

for you to find x you first have to find the adjacent of the 45° angle you can do that by using the other triangle.using the sin ratio

sin60=opposite/hypotenuse

sin60=a/7√3

a=10.5

then after you have found the adjacent you can use the cos ratio

cos45=adjacent/hypotenuse

cos45=10.5/x

cos45x/cos45=10.5/cos45

x=14.849

which is the same as 21√2 over 2

I hope this helps