Use the given sine ratio formula.

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9. In a right-angled triangle, the opposite side to an angle is 7 cm and the hypotenuse is 14 cm. Using the sine ratio ( $\sin \theta = \text{opposite/hypotenuse}$ ), find the angle to the nearest degree.

Use the given sine ratio formula.
$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$
Substitute the given values into the formula.
$\sin \theta = \frac{7 \text{ cm}}{14 \text{ cm}}$
Simplify the fraction.
$\sin \theta = \frac{1}{2}$
To find the angle $\theta$ , take the inverse sine (arcsin) of $\frac{1}{2}$ .
$\theta = \arcsin\left(\frac{1}{2}\right)$ $\theta = 30^\circ$
The angle to the nearest degree is $\boxed{\text{}30^\circ\text{}}$

10. A surveyor needs to find the height of a building. She stands 50 metres away from the base of the building and measures the angle of elevation to the top as $35^\circ$ .
This problem forms a right-angled triangle where the height of the building is the opposite side to the angle of elevation, and the distance from the base is the adjacent side.
We use the tangent ratio: $\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$ .
Let $h$ be the height of the building.
$\tan 35^\circ = \frac{h}{50 \text{ m}}$
Multiply both sides by 50 m to solve for $h$ .
$h = 50 \text{ m} \times \tan 35^\circ$
Calculate the value of $\tan 35^\circ$ and then multiply.
$h \approx 50 \text{ m} \times 0.7002$ $h \approx 35.01 \text{ m}$
The height of the building is approximately $\boxed{\text{}35.0 \text{ m}\text{}}$

Use the given sine ratio formula.

Step-by-step solution

Use the given sine ratio formula.

Substitute the given values into the formula.

Simplify the fraction.

To find the angle $\theta$ , take the inverse sine (arcsin) of $\frac{1}{2}$ .

This problem forms a right-angled triangle where the height of the building is the opposite side to the angle of elevation, and the distance from the base is the adjacent side.

Multiply both sides by 50 m to solve for $h$ .

Calculate the value of $\tan 35^\circ$ and then multiply.

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More Mathematics Questions

Use the given sine ratio formula.

Step-by-step solution

Use the given sine ratio formula.

Substitute the given values into the formula.

Simplify the fraction.

To find the angle θ\thetaθ, take the inverse sine (arcsin) of 12\frac{1}{2}21​.

This problem forms a right-angled triangle where the height of the building is the opposite side to the angle of elevation, and the distance from the base is the adjacent side.

Multiply both sides by 50 m to solve for hhh.

Calculate the value of tan⁡35∘\tan 35^\circtan35∘ and then multiply.

Still stuck on this one?

More Mathematics Questions

To find the angle $\theta$ , take the inverse sine (arcsin) of $\frac{1}{2}$ .

Multiply both sides by 50 m to solve for $h$ .

Calculate the value of $\tan 35^\circ$ and then multiply.