Question: x
30cm
15cm
x= __________ degrees
(In 2 sig figs)
Graph: a right triangle with the right angle at the bottom-right, base labeled 15cm along the bottom, vertical side labeled 30cm on the right, and the angle x marked at the top between the slanted side and the vertical side; position_hint=center
1. **State the problem:** We have a right triangle with a vertical side of length $30$ cm, a base of length $15$ cm, and we want to find the angle $x$ between the slanted side (hypotenuse) and the vertical side.
2. **Identify the sides relative to angle $x$:** The side opposite angle $x$ is the base $15$ cm, and the side adjacent to angle $x$ is the vertical side $30$ cm.
3. **Use the tangent function:** $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{15}{30}$$
4. **Simplify the fraction:** $$\tan(x) = \frac{15}{30} = \frac{\cancel{15}}{\cancel{30}} = \frac{1}{2}$$
5. **Find the angle $x$ by taking the arctangent:** $$x = \tan^{-1}\left(\frac{1}{2}\right)$$
6. **Calculate the value:** Using a calculator, $$x \approx 26.5651^\circ$$
7. **Round to 2 significant figures:** $$x \approx 27^\circ$$
**Final answer:** $x = 27^\circ$ (to 2 significant figures).