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4 votes
X

Solve for x.
10 cm
20°
X = [?] cm
Round to the nearest hundredth

User Tdehaeze
by
8.6k points

2 Answers

4 votes

The length of the side, x, in the given right-angled triangle with a hypotenuse length of 10 cm is 6.82 cm.

The challenge asks us to calculate the length of a right triangle's missing side. The data provided are the length of one leg (10 cm) and the measurement of one of the acute angles (20°).

To find the missing side, we can utilize the sine function. The sine function is the ratio of a right triangle's opposing side to its hypotenuse.

The opposing side is the missing side in this situation, while the hypotenuse is the side opposite the right angle.

To calculate x, use the following equation:

sin(20°) = x / 10

We can find x by multiplying both sides of the equation by 10 and then evaluating the statement with a calculator. The solution is x = 6.82 cm.

We can use the following methods to round the answer to the nearest hundredth:

Find the answer's hundredths place, which is 2.

Look at the number 8 to the right of the hundredths spot.

The hundredths place is rounded up if the digit to the right of the hundredths place is 0, 1, 2, 3, 4, or 5.

The hundredths place is rounded up to the next number if the digit to the right of the hundredths place is 6, 7, 8, or 9.

Because the figure to the right of the hundredths place in this case is 8, the hundredths place is rounded up to 9. As a result, the rounded solution is x = 6.82 cm.

X Solve for x. 10 cm 20° X = [?] cm Round to the nearest hundredth-example-1
User Gladen
by
8.8k points
4 votes
I'm assuming that you have a right triangle with one acute angle of 20 degrees and the side opposite to this angle is of length 10 cm.

To solve for x, we can use the following trigonometric ratio:

tan(20) = opposite / adjacent

In this case, the opposite side is 10 cm and we want to find the adjacent side, which is x. Therefore, we can rearrange the equation to solve for x:

x = opposite / tan(20) = 10 / tan(20) ≈ 28.74 cm

Rounding to the nearest hundredth, x ≈ 28.74 cm becomes x ≈ 28.73 cm. Thus, the length of x is approximately 28.73 cm.
User Evk
by
7.8k points

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