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Find Hypotenuse of Right Triangle with Legs 7 and 15 (Round to Nearest Tenth)
Mathematics
Grade 10 (High School Geometry)
Question Content
Use the diagram (right triangle MPN with right angle at P, PN=15, MP=7) to find the length of MN. Round your answer to the nearest tenth.
Correct Answer
16.6
Detailed Solution Steps
1
Step 1: Recognize that triangle MPN is a right triangle, so we can use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse (MN) and $a, b$ are the legs (MP=7, PN=15).
2
Step 2: Substitute the known values into the formula: $7^2 + 15^2 = MN^2$.
3
Step 3: Calculate the squares: $49 + 225 = MN^2$, so $274 = MN^2$.
4
Step 4: Take the square root of both sides: $MN = \\sqrt{274} \\approx 16.6$.
Knowledge Points Involved
1
Pythagorean Theorem
The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Formula: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse. It is used to find unknown side lengths in right triangles when two sides are known.
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