SAT Right triangles and trigonometry Practice Question 4 (Medium)

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

A $20$ -foot ladder leans against a vertical wall, and the ladder makes a $70^\circ$ angle with the level ground. Which expression represents the height, in feet, at which the top of the ladder touches the wall?

$20\cos 70^\circ$

$20\tan 70^\circ$

$20\sin 70^\circ$

$\frac{20}{\sin 70^\circ}$

Show answer and explanation

Answer: C

The ladder is the hypotenuse of a right triangle, and the height on the wall is the side opposite the $70^\circ$ angle. Since $\sin 70^\circ = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{20}$ , the height is $h = 20\sin 70^\circ$ .

Choice A gives the distance from the wall to the base of the ladder, which is the side adjacent to the $70^\circ$ angle.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.