Question: Help: PDF Ex. 19.2 Video Ex. 19.2 Hint: Use $\sin^{-1}$ to find angle $A$, then $B = 90 - A$
13.19 Find the missing angles. Round to 1 d.p.
If needed, see "I'm Stuck"
Instructions: Type answer like an ordered pair $A,B$ no parentheses, no spaces between characters.
Round to 1 decimal place. For example: $30.2,59.8$ or $40.5,49.5$
Answer: 4
Graph shape: a right triangle in the top-right, with the right angle at the top-left, the top side labeled $7.1$, the slanted side labeled $8.9$, angle $A$ at the bottom-left, and angle $B$ at the right vertex. Position hint: top-right
1. **Problem Statement:** We have a right triangle with a right angle at the top-left vertex. The side opposite angle $A$ (bottom-left) is $7.1$, and the hypotenuse (slanted side) is $8.9$. We need to find the missing angles $A$ and $B$ rounded to 1 decimal place.
2. **Formula and Rules:** In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse:
$$\sin A = \frac{\text{opposite}}{\text{hypotenuse}}$$
Since the triangle is right angled, the other acute angle $B$ satisfies:
$$B = 90^\circ - A$$
3. **Calculate angle $A$:**
$$\sin A = \frac{7.1}{8.9}$$
Calculate the fraction:
$$\frac{7.1}{8.9} \approx 0.7978$$
Now find $A$ using inverse sine:
$$A = \sin^{-1}(0.7978)$$
Using a calculator:
$$A \approx 52.8^\circ$$
4. **Calculate angle $B$:**
$$B = 90^\circ - 52.8^\circ = 37.2^\circ$$
5. **Final answer:**
$$A,B = 52.8,37.2$$
This matches the instructions to round to 1 decimal place and format as an ordered pair without spaces or parentheses.