Math / Trigonometry

Question4. Below is a right-angled triangle.
Use trigonometry to work out the length x .

Studdy Solution

STEP 1

1. The triangle is a right-angled triangle.
2. The angle given is $36^\circ$ .
3. The side opposite the $36^\circ$ angle is labeled $x$ .
4. The hypotenuse is $7 \text{ cm}$ .

STEP 2

1. Identify the appropriate trigonometric ratio.
2. Set up the equation using the trigonometric ratio.
3. Solve for $x$ .

STEP 3

Identify the appropriate trigonometric ratio. Since we have the angle and need to find the opposite side, and we know the hypotenuse, we use the sine function:
$\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$

STEP 4

Set up the equation using the sine function:
$\sin(36^\circ) = \frac{x}{7}$

STEP 5

Solve for $x$ :
$x = 7 \times \sin(36^\circ)$
Calculate $\sin(36^\circ)$ using a calculator:
$\sin(36^\circ) \approx 0.5878$
Substitute back into the equation:
$x \approx 7 \times 0.5878$ $x \approx 4.1146$
The length of $x$ is approximately:
$\boxed{4.11 \text{ cm}}$

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