IXL - Trigonometric ratios: word problems (Algebra 2 practice)

Rivertown Mall's manager is installing a string of holiday lights along the escalator. She needs to know how long the escalator is. The escalator makes a

angle with the ground, and the upper level is 10 meters above the ground level. How long is the escalator?

Round your answer to the nearest meter.

meters

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Learn with an example

question

Heather is one of the architects working on plans for a new hotel. The second floor will be 22 feet above the ground floor, and the hotel will have an escalator connecting the ground floor and the second floor. The escalator will make a

angle with the ground. How long will the horizontal base of the escalator be along the ground floor?

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 the length of the horizontal base of the escalator along the ground floor, first recall the given information:

The second floor will be 22 feet above the ground floor.
The escalator will make a
32
°
angle with the ground.

Use a diagram to represent this information. Let represent the length of the horizontal base of the escalator.

Notice that we know the measure of an acute angle in a right triangle and its opposite leg, and is its adjacent leg.

Since tangent is the ratio of the length of the opposite leg to the length of the adjacent leg, use

tan

to find

tan

35.2073…

The length of the horizontal base of the escalator along the ground floor will be about 35

feet.

Looking for more? Try this:

Lesson: Trigonometric ratios

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Work it out

Not feeling ready yet? These can help:

II.16Trigonometric ratios: find a side length

II.17Trigonometric ratios: find an angle measure

Lesson: Trigonometric ratios

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