Question

determine the length of x and y to the nearest tenth of a centimetre.
4.5 cm
x = 6 cm, y = 8 cm
x = 6.2 cm, y = 7.7 cm
x = 6.6 cm, y = 8 cm
x = 6.4 cm, y = 7.8 cm

Explanation:

Step1: Find x using tangent function

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 55^{\circ}$ and the opposite side to $\theta$ is $x$, the adjacent side is $4.5$ cm. So $\tan(55^{\circ})=\frac{x}{4.5}$, then $x = 4.5\times\tan(55^{\circ})$. Since $\tan(55^{\circ})\approx1.4281$, $x=4.5\times1.4281 = 6.42645\approx6.4$ cm.

Step2: Find y using cosine function

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here $\theta = 55^{\circ}$, the adjacent side is $4.5$ cm and the hypotenuse is $y$. So $\cos(55^{\circ})=\frac{4.5}{y}$, then $y=\frac{4.5}{\cos(55^{\circ})}$. Since $\cos(55^{\circ})\approx0.5736$, $y=\frac{4.5}{0.5736}\approx7.8452\approx7.8$ cm.

Answer:

D. $x\approx6.4$ cm, $y\approx7.8$ cm