Questions: Draw the altitude from vertex A in each of the triangles. Then use trigonometry to find the height of the altitude. Leave your answer in terms of sin θ, cos θ, or tan θ. (Hint: Answer will look something like this: H=n sin θ )

Solution Steps

For each triangle, draw the altitude from vertex \( A \) to the base \( BC \). This altitude will form a right angle with \( BC \).

For each triangle, identify the trigonometric function that relates the given angle to the altitude. The altitude will be opposite the given angle.

Use the sine function, which relates the opposite side (altitude) to the hypotenuse in a right triangle.

• Given: \( \angle B = 45^\circ \), \( BC = 10 \)
• Use \( \sin 45^\circ = \frac{\text{altitude}}{BC} \)
• \( \sin 45^\circ = \frac{h}{10} \)
• \( h = 10 \sin 45^\circ \)

• Given: \( \angle B = 39^\circ \), \( AB = 18 \)
• Use \( \sin 39^\circ = \frac{\text{altitude}}{AB} \)
• \( \sin 39^\circ = \frac{h}{18} \)
• \( h = 18 \sin 39^\circ \)

Final Answer