SAT Right Triangles & Trigonometry Question 43 | Free SAT Prep | Aniko

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Question 43·Easy·Right Triangles and Trigonometry

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A wheelchair ramp forms a right triangle with the ground. The ramp is 13 feet long, and the horizontal distance from the bottom of the ramp to the wall is 12 feet. Let $\theta$ be the angle the ramp makes with the ground.

What is the value of $\cos\theta$ ?

For right-triangle trig questions, identify the hypotenuse first (the longest side, opposite the right angle). Then, relative to $\theta$ , decide which given side is adjacent. Apply $\cos\theta=\dfrac{\text{adjacent}}{\text{hypotenuse}}$ .

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Recall what cosine means

In a right triangle, $\cos\theta=\dfrac{\text{adjacent}}{\text{hypotenuse}}$ .

Find the hypotenuse

The hypotenuse is the side opposite the right angle. In this situation, it is the ramp (the longest side).

Find the adjacent side

The adjacent side is the leg next to $\theta$ that is not the hypotenuse. Here, it is the horizontal distance along the ground.

Desmos Guide

Compute the cosine ratio

Enter the fraction $12/13$ into Desmos to get its decimal value.

Match to the choices

Choose the answer option that equals the fraction you entered, which is $\frac{12}{13}$ .

Step-by-step Explanation

Identify adjacent and hypotenuse

The ramp length (13 feet) is the hypotenuse. The horizontal distance along the ground (12 feet) is the side adjacent to $\theta$ .

Use the cosine ratio

By definition,

\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{12}{13}.

So, $\cos\theta=\frac{12}{13}$ .

Strategy

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Desmos Guide

Step-by-step Explanation

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Step-by-step Explanation