Question

What are the missing sides in the triangle written as integers or as decimals rounded to the
nearest tenth? The figure is not drawn to scale.

x= 18; y = 15.6
x= 12.7; y = 15.6
x= 12.7;y=9
x=9; y = 12.7

Answer 1

The value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9

Trigonometry

From the question, we are to determine the values of the missing sides

From the diagram,

Opposite = 9

Adjacent = y

Hypotenuse = x

Included angle = 45°

Using SOH CAH TOA, we can write that

$tan 45^\circ= \frac{9}{y}$

$1 = \frac{9}{y}$

∴ y = 9

Since the triangle is a right triangle, we can write that

x² = y² + 9² (Pythagorean theorem)

x² = 9² + 9²

x² = 81 + 81

x² = 162

x = √162

x = 12.7

Hence, the value of x is 12.7 and the value of y is 9. The correct option is the third option x = 12.7; y = 9

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