IXL - Trigonometric ratios: word problems (Precalculus practice)

Madelyn is building a ramp for her brother to use with his toy cars. She is building the ramp to make a

angle with the ground. If the board she is using for the ramp itself is 85 centimeters long, what is the horizontal distance she will need for the ramp?

Round your answer to the nearest centimeter.

centimeters

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Learn with an example

question

The custodian at Jackson Middle School wants to hang the new school banner in the lunchroom. He uses a 20-foot ladder, which is placed at a

angle with the ground. How high up the wall of the lunchroom will the ladder reach?

Round your answer to the nearest foot.

feet

key idea

Trigonometric ratios in a right triangle

The sine (sin) of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse.

The cosine (cos) of an acute angle in a right triangle is the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse.

The tangent (tan) of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle.

sin

(

)

opposite

hypotenuse

cos

(

)

adjacent

hypotenuse

tan

(

)

opposite

adjacent

solution

To find how far up the wall of the lunchroom the ladder will reach, first recall the given information:

The ladder is 20 feet long.
It will be placed at a
75
°
angle with the ground.

Use a diagram to represent this information. Let

represent the height up the wall the ladder reaches.

Notice that we know the measure of an acute angle in a right triangle and the hypotenuse, and

is the leg opposite that angle.

Since sine is the ratio of the length of the opposite leg to the length of the hypotenuse, use

sin

to find

sin

19.3185…

The ladder will reach about 19 feet up the lunchroom wall.

Looking for more? Try this:

Lesson: Trigonometric ratios

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Not feeling ready yet? These can help:

R.12Trigonometric ratios: find a side length

R.13Trigonometric ratios: find an angle measure

Lesson: Trigonometric ratios

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