Question

the opposite side of a right triangle is 16 cosθ meters, whereas the adjacent side is 16 sinθ meters. calculate the length of the hypotenuse in centimeters.
a 1
b 4
c 16
d 256
e 1600

Explanation:

Step1: Use Pythagorean theorem

For a right - triangle with legs \(a = 16\cos\theta\) and \(b = 16\sin\theta\), the Pythagorean theorem states \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=(16\cos\theta)^{2}+(16\sin\theta)^{2}\).

Step2: Expand the squares

$$
LATEXBLOCK0
$$

Step3: Use the trigonometric identity \(\cos^{2}\theta+\sin^{2}\theta = 1\)

Since \(\cos^{2}\theta+\sin^{2}\theta = 1\), then \(c^{2}=256\times1\), so \(c = 16\) meters.

Step4: Convert meters to centimeters

Since \(1\) meter \(= 100\) centimeters, then \(16\) meters \(=16\times100=1600\) centimeters.

Answer:

E. 1600