Question

Consider the diagram below.

450
х
45°
7
Which of the following is the value of x?

Answer 1

C

Explanation:

using the sin ratio in the lower right triangle and the exact value

sin45° =
`(1)/(√(2) )` , then

sin45° =
`(opposite)/(hypotenuse)` =
`(7)/(y)` =
`(1)/(√(2) )` [ y represents the hypotenuse ]

cross- multiplying gives

y = 7
`√(2)`

------------------------------------------

using the sine ratio in the upper right triangle

sin45° =
`(opposite)/(hypotenuse)` =
`(y)/(x)` =
`(7√(2) )/(x)` =
`(1)/(√(2) )` ( cross- multiply )

x = 7
`√(2)` ×
`√(2)` = 7 × 2 = 14