Question

6
select the correct answer.
what is the value of x?
triangle with right angle, 45° angle, hypotenuse 15, side x
a. 21.2
b. 7.5
c. 15
d. 10.6
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Explanation:

Step1: Determine the type of triangle

This is a right - angled triangle with one angle \(45^{\circ}\), so it is a \(45 - 45-90\) triangle. In a \(45 - 45 - 90\) triangle, the sides are in the ratio \(1:1:\sqrt{2}\). Let the legs be \(a\) and \(a\), and the hypotenuse be \(c\). Here \(c = 15\).

Step2: Use the sine formula

We know that \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\theta = 45^{\circ}\), \(\sin45^{\circ}=\frac{x}{15}\). Since \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\), then \(x = 15\times\sin45^{\circ}\).

$$x=15\times\frac{\sqrt{2}}{2}=\frac{15\sqrt{2}}{2}\approx\frac{15\times1.414}{2}=\frac{21.21}{2}=10.605\approx10.6$$

Answer:

D. 10.6