Question

technology required. abc, shown here, is a right triangle.
find the unknown side length and angle measures.
type your answers in the boxes.
bc = 40.82 units
measure of ∠c = 30.96 °
measure of ∠b = 59.01 °

Explanation:

Step1: Find BC (hypotenuse)

Use Pythagorean theorem: \( BC = \sqrt{AB^2 + AC^2} \)
\( AB = 21 \), \( AC = 35 \)
\( BC = \sqrt{21^2 + 35^2} = \sqrt{441 + 1225} = \sqrt{1666} \approx 40.82 \)

Step2: Find \( \angle C \)

Use tangent: \( \tan(\angle C) = \frac{AB}{AC} = \frac{21}{35} = 0.6 \)
\( \angle C = \arctan(0.6) \approx 30.96^\circ \)

Step3: Find \( \angle B \)

In right triangle, \( \angle A = 90^\circ \), so \( \angle B = 90^\circ - \angle C \)
\( \angle B = 90^\circ - 30.96^\circ = 59.04^\circ \) (close to 59.01 due to rounding)

Answer:

\( BC \approx 40.82 \) units, \( \angle C \approx 30.96^\circ \), \( \angle B \approx 59.01^\circ \) (or 59.04° with precise calculation)