Gloria wants to find the length of segment N P. Which set of steps will give her the correct length?
1. Find segment M P using the equation cos 60° = M P / 31.
2. Find segment N P using the Pythagorean theorem, M N² = M P² + N P².

1. Add 25° + 60°, and then subtract the result from 180° to find m∠M.
2. Find segment M P using the equation tan M = N P / M P.

1. Find segment M P using the equation tan 25° = M P / 31.
2. Find segment N P by subtracting segment L P from segment L N.

Question

Gloria wants to find the length of segment N P. Which set of steps will give her the correct length?
1. Find segment M P using the equation cos 60° = M P / 31.
2. Find segment N P using the Pythagorean theorem, M N² = M P² + N P².

1. Add 25° + 60°, and then subtract the result from 180° to find m∠M.
2. Find segment M P using the equation tan M = N P / M P.

1. Find segment M P using the equation tan 25° = M P / 31.
2. Find segment N P by subtracting segment L P from segment L N.

Quizzma Team · Answer

To solve for the length of segment NP, the best set of steps is the following:

1. Find segment MP using the equation tan 25° = MP / 31.

This step allows Gloria to find the length of segment MP based on the angle given and the length of the adjacent segment (which in this case is 31).

2. Find segment NP using the Pythagorean theorem, MN² = MP² + NP².

Once MP is known, she can use the Pythagorean theorem to find NP since MN is a right triangle.

### Explanation:

The first step uses tangent to relate the opposite and adjacent sides of a right triangle, resulting in the length of segment MP. The second step then applies the Pythagorean theorem, which is appropriate for any right triangle, to solve for NP. This method is systematic and uses the principles of trigonometry effectively.

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Quizzma Team · Answer

To find the correct length of segment N P, we can use the first set of steps, which apply the cosine and the Pythagorean theorem correctly.

1. Find segment M P using the equation ( cos 60° = frac{M P}{31} ). This equation allows us to find the length of segment M P based on the given angle and the hypotenuse (31).

2. Find segment N P using the Pythagorean theorem: ( M N² = M P² + N P² ). This step helps in finding the length of N P when we have the length of M P.

In summary, the first set of steps is the correct method to determine the length of segment N P, since it appropriately combines trigonometric functions and the Pythagorean theorem.

2 Answers