Question

If a=38° and y=42 cm, what is the value of x to the nearest tenth of a centimeter

Answer 1

The value of x to the nearest tenth of a centimeter is 25.2 cm.

Given:

∠a = 38°

Hypotenuse y = 42 cm

To Find:

The measure of perpendicular x

Solution:

The given triangle is a right-angled triangle.

In which one angle is 90° and sides containing 90° are base and perpendicular.

We can apply sin(a) to find the measure of perpendicular x.

$\implies sin(a) = \frac{P}{H} \\\\\implies sin(38^{\circ}) = \frac{x}{y} \\\\\implies 0.6 = \frac{x}{y}\\\\\implies 0.6 = \frac{x}{42} \\\\\implies 0.6 \tims 42 = x\\\\\implies x = 25.2cm$

Therefore, perpendicular x to the nearest tenth of a centimeter is 25.2cm

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Answer 2

Answer:

The value of $x$ to the nearest tenth of a centimeter is $25.83 cm$.

How to round to the nearest tenth?

We have to review rounding on a number line, need to write down a number with a decimal point, then find the tenth place, look at the hundredths place and then round the tenths place up if the hundredths place is $5$ or more

Explanation

It is given that the angle $\alpha =38{}^\circ$ and,

$y=42\text{ cm}$.

It is required to find the value of $x$ nearest tenth of a centimeter.

To find the value of $x$, we will use the trigonometric formula and simplify it.

According to the trigonometric rule,

$\sin \text{ }\!\!\theta\!\!\text{ =}\frac{\text{opposite side}}{\text{hypotenuse}}$

Let,

$\sin \left( \alpha \right)=\frac{x}{y}$

Here, $x$ is the opposite side and $y$ is the hypotenuse.

Substitute the given values in the above formula. We get,

 $\text{sin }\left( \alpha \right)\text{=}\frac{x}{y}$

$\sin \left( 38{}^\circ \right)=\frac{x}{42}$

The value of $\sin \left( 38{}^\circ \right)$ is $0.615$.

So,

       $0.615=\frac{x}{42}$

$0.615\times 42=x$

             $x=25.83$

Round to the nearest tenth, we get $25.8$.

Hence, the value of $x$ is 25.83 cm.

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