A right triangle’s hypotenuse is 20 cm long. What is the length of the side opposite a 60° angle? Give your answer to the nearest tenth of a centimeter.

• 40
• 18.5
• 20
• 17.3
Please show how.

The sides are in the ratio 1:√3:2, so with the hypotenuse=20, we have

10:10√3:20, with the longer leg opposite the larger angle.

Looks like 17.3 to me.

Thanks much

Why did the triangle go to the beach?

Because it wanted to find its beach side!

Now, let's solve this math problem.

We have a right triangle with a hypotenuse of 20 cm. To find the length of the side opposite a 60° angle, we can use trigonometry.

The side opposite the 60° angle is usually called the "opposite side". In this case, we'll call it "x".

We can use the sine function to find x:
sin(60°) = x / 20

To find x, we can rearrange the equation:
x = 20 * sin(60°)

Using a calculator, we find that sin(60°) is approximately 0.866.
So, x = 20 * 0.866 = 17.3

So, the length of the side opposite the 60° angle is approximately 17.3 cm.

Therefore, the answer is 17.3.

Hope this helps!

To find the length of the side opposite a 60° angle in a right triangle, we can use the trigonometric relationship known as the sine function.

The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse. The formula is:

sin(θ) = opposite / hypotenuse

We can rearrange this formula to solve for the length of the opposite side:

opposite = sin(θ) * hypotenuse

In this case, the angle is 60° and the hypotenuse is 20 cm. Plugging these values into the formula, we get:

opposite = sin(60°) * 20

Using a calculator, we find that sin(60°) is approximately 0.866. So,

opposite = 0.866 * 20

Calculating this, we get:

opposite ≈ 17.3 cm

Therefore, the length of the side opposite the 60° angle is approximately 17.3 cm. The answer is option D: 17.3.

To find the length of the side opposite a 60° angle in a right triangle, you can use the trigonometric function sine (sin).

In a right triangle, sin(angle) = opposite/hypotenuse.

In this case, the hypotenuse is given as 20 cm, and the angle is 60°.

So, sin(60°) = opposite/20.

To find the value of sin(60°), you can use a calculator or table of trigonometric values. Sin(60°) is approximately 0.866.

Now, we can substitute the known values into the equation:

0.866 = opposite/20.

To solve for the length of the opposite side, multiply both sides of the equation by 20:

0.866 * 20 = opposite.

The calculation gives us:

opposite = 17.32 cm.

Rounded to the nearest tenth of a centimeter, the length of the side opposite the 60° angle is approximately 17.3 cm.

Therefore, the correct answer is 17.3 cm.