Banzell, this is the solution:
Left triangle:
• Hypotenuse = 23
,• Leg 1 = 15
,• Leg 2 = a
Using the Pythagorean theorem, we can find Leg 2, this way:
Leg 2² = 23² - 15²
Leg 2² = 529 - 225
Leg 2² = 304
Square root at both sides:
√Leg 2 ² = √304
Leg 2 = 17.44
Now, we can find the measure of x, as follows:
x = arcsin (15/23)
x = arcsin (0.6522)
x = 0.71045 rad
x = 40.7 degrees
Right triangle:
• Hypotenuse = h
,• Leg 1 = 8
,• Leg 2 = 37
Using the Pythagorean theorem, we can find the Hypotenuse, this way:
h² = 8² + 37²
h² = 64 + 1,369
h² = 1,433
Square root at both sides:
√h² = √1,433
h = 37.86
Now, let's calculate the measure of x, this way:
x = arcsin (37/37.86)
x = arcsin (0.9773)
x = 1.358 rad
x = 77.8 degrees
In consequence, the bigger angle is the one from the triangle on the right.
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