Question: Look at the diagram of a high school pole vaulter in action. To hit their potential they need to make sure they are holding the pole at the correct angle.
At takeoff, a° = 23°. What is c°, the measure of the angle the pole makes with the athlete's body?
113
67
23
58
1. **State the problem:** We are given a right triangle with angles including $a = 23^\circ$ and need to find $c^\circ$, the angle the pole makes with the athlete's body.
2. **Understand the angles:** The problem involves a triangle with angles $a$, $b$, and $c$. Since the pole and athlete's body form an exterior angle $c$, and $a$ is given, we use the exterior angle theorem.
3. **Exterior angle theorem:** The exterior angle $c$ equals the sum of the two opposite interior angles. Here, $c = a + b$.
4. **Given angles:** From the diagram, one angle is $a = 23^\circ$ and another angle is $58^\circ$ (likely $b$).
5. **Calculate $c$:**
$$
c = a + b = 23^\circ + 58^\circ = 81^\circ
$$
6. **Check options:** The options are 113, 67, 23, and 58. Since $81^\circ$ is not listed, reconsider the interpretation.
7. **Alternative approach:** The pole forms an angle $c$ with the athlete's body, and $a = 23^\circ$ is the angle between the pole and the ground. The angle between the athlete's body (vertical) and the ground is $90^\circ$.
8. **Calculate $c$ using complementary angles:**
$$
c = 90^\circ - a = 90^\circ - 23^\circ = 67^\circ
$$
9. **Final answer:** $c = 67^\circ$.
This matches one of the options.
**Answer: 67**