Using the Pythagorean theorem and the law of sines, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are: A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°
What is the Pythagorean Theorem?
The theorem states that the square of the longest side of a right triangle equals the sum of the squares of the lengths of the other two smaller sides of the right triangle.
The points, M(3,2), E(3,−3), and R(9,−3) has been plotted on the graph which shows that angle E is a right triangle, therefore:
m∠E = 90 degrees.
Find ME and ER:
ME = 5 units
ER = 6 units.
Using the Pythagorean theorem, find MR:
MR = √(ME² + ER²)
MR = √(5² + 6²)
MR = √(25 + 36)
MR = 7.81 units
Using the law of sines, find m∠M:
sin M/ER = sin E/MR
sin M/6 = sin 90/7.81
sin M = (sin 90 × 6)/7.81
sin M = 0.7682
M = sin^(-1)(0.7682)
m∠M ≈ 50°
m∠R = 180 - 50 - 90
m∠R = 40°
Thus, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are:
A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°
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