Answer:
Measure of angle A = 55.00 degrees
Length of side b = 14.34
Length of side a = 20.48
Explanation:
Step 1: Find the measure of angle A:
- The Triangle Sum Theorem says that the sum of a triangle's interior angles equals 180°.
Since a right angle is 90°, we can subtract the sum of the right angle and the 35° angle from 180 to find the measure of angle B:
m∠A + m∠B + m∠C = 180°
m∠A = 180 - (m∠B + m∠C)
m∠A = 180 - (35 + 90)
m∠A = 180 - 125
m∠A = 55
Thus, the measure of angle A rounded to two decimal places is 55.00°.
Since your answer box already has the units, simply write 55.00 as your answer.
Step 2: Find the length of side b:
- Since this is a right triangle, we can find the length of side b using one of the trigonometric ratios.
When the 35° angle is the reference angle:
- side b is the opposite side,
- and side c (i.e., the 25-units long side) is the hypotenuse.
Thus, we can find the length of side b using sine ratio, whose general equation is given by:
sin (θ) = opposite / hypotenuse, where
- θ is the reference angle.
Thus, we can find the length of side b (aka the opposite side in the sine ratio) by substituting 35 for θ and 25 for the hypotenuse in the sine ratio:
(sin (35) = b / 25) * 25
25 * sin (35) = b
14.33941091 = b
14.34 = b
Thus, side b is about 14.34 units long.
Step 3: Find the length of side a:
- We can again use one of the trigonometric ratios to find the length of side a.
When the 35° angle is the reference angle:
- side a is the adjacent side,
- and side c is the hypotenuse.
Thus, we can find the length of side a using the cosine ratio, whose general equation is given by:
cos (θ) = adjacent / hypotenuse, where
- θ is the reference angle.
Thus, we can find the length of side a by substituting 35 for θ and 25 for the hypotenuse in the cosine ratio:
(cos (35) = a / 25) * 25
25 * cos (35) = a
20.47880111 = a
20.48 = a
Thus, the length of side a is about 20.48 units.