Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Use the tangent ratio to find the missing leg of this right triangle. Estimate your answer to two decimal places.

Use the tangent ratio to find the missing leg of this right triangle. Estimate your answer to two decimal places.

View step-by-step help

View step-by-step help

Circles: word problems

Full solution

Q. Use the tangent ratio to find the missing leg of this right triangle. Estimate your answer to two decimal places.

Write Tangent Ratio Formula: Write down the tangent ratio formula, which is $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ .
Identify Angle and Sides: Identify the angle $\theta$ and the lengths of the sides given in the problem. Let's say the angle $\theta$ is $35$ degrees, the opposite side is the missing leg we need to find, and the adjacent side is $7\,\text{cm}$ .
Plug Values into Formula: Plug the values into the tangent ratio formula. So, $\tan(35^\circ) = \frac{\text{missing leg}}{7\,\text{cm}}$ .
Calculate Tangent Value: Use a calculator to find the value of $\tan(35^\circ)$ . Let's say $\tan(35^\circ) \approx 0.70$ .
Isolate Missing Leg: Multiply both sides by $7\,\text{cm}$ to isolate the missing leg. So, missing leg $= 7\,\text{cm} \times \tan(35) \approx 7\,\text{cm} \times 0.70$ .
Calculate Missing Leg Length: Calculate the approximate length of the missing leg. Missing leg $\approx 7 \, \text{cm} \times 0.70 \approx 4.90 \, \text{cm}.$

More problems from Circles: word problems

Question

Skyler climbs a watchtower to guard against forest fires.

\newline

R(h)=\sqrt{13h}

gives the distance, in kilometers, that Skyler can see when their eyes are

h

meters above the ground.

\newline

A(d)=\pi d^{2}

gives the area, in square kilometers, that Skyler can guard when they can see a distance of

d

\newline

Which expression models the area Skyler can guard when their eyes are

h

meters above the ground?

\newline

1

\newline

13\pi h

\newline

13\pi h^{2}

\newline

\sqrt{13\pi h^{2}}

\newline

169\pi h^{2}

Posted 2 months ago

Question

After the outbreak of a mysterious disease, the average wait time at a hospital increased by

70\%

. Before the outbreak, the average wait time at the hospital was

m

\newline

Which of the following expressions could represent the average wait time at the hospital after the outbreak?

\newline

2

\newline

0.7m

\newline

\frac{170}{100}m

\newline

m+70

\newline

m+0.7

\newline

1.7m

Posted 1 month ago

Question

The radius of a semicircle is

3

yards. What is the semicircle's area?

\newline

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

Posted 2 months ago

Question

\newline

A man has bent a circular wire of radius

49\text{cm}

to form a square. Find the sides of a square.

\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

Posted 2 months ago

Question

A quarter is worth

\$0.25

and a half dollar is worth

\$0.50

\newline

a. A quarter has a diameter of

\frac{15}{16}

inch and a height of

\frac{1}{16}

inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.

\newline

b. A half dollar has a diameter of

\frac{9}{8}

inches and a height of

\frac{3}{32}

inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.

Posted 2 months ago

Question

The hypotenuse of a right triangle measures

17 \mathrm{~cm}

and one of its legs measures

8 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

One of the legs of a right triangle measures

15 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

One of the legs of a right triangle measures

8 \mathrm{~cm}

and the other leg measures

15 \mathrm{~cm}

. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 2 months ago

Question

Find the volume of a right circular cone that has a height of

7.4 \mathrm{~cm}

and a base with a radius of

8.1 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

\mathrm{cm}^{3}

Posted 2 months ago

Question

Find the volume of a right circular cone that has a height of

13.3 \mathrm{ft}

and a base with a diameter of

9.4 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

\mathrm{ft}^{3}

Posted 2 months ago