Question

!50 POINTS! (1 SIMPLE GEOMETRY QUESTION)

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Answer 1

d) 87.7 ft

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Explanation:

The given diagram shows a right triangle, where the base of the triangle is b ft, the angle between the height of the triangle and the hypotenuse is 38°.

To find the length of the six cars, we need to find the length of the hypotenuse of the right triangle.

To do this we can use the sine trigonometric ratio, since we have the side opposite the angle, and wish to find the hypotenuse.

`\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=(O)/(H)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

Given values:

• θ = 38°
• O = b = 54 ft
• H = H (to be found)

Substitute the given values into the sine ratio and solve for H:

`\begin{aligned}\sin 38^(\circ)&=(54)/(H)\\\\H}&=(54)/(\sin 38^(\circ))\\\\H}&=87.710539...\\\\H}&=87.7\; \sf ft\;(nearest\;tenth)\end{aligned}`

Therefore, the total length of the six cars is approximately 87.7 ft (rounded to the nearest tenth).