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Which of the two is the bigger degree? what is the measure?

Which of the two is the bigger degree? what is the measure?-example-1
User Pawara Siriwardhane
by
3.1k points

1 Answer

23 votes
23 votes

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.

User Techvslife
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2.7k points