Question

8.2b - pythagorean theorem
for each right triangle, find the length of the missing side that is not given. round to the nearest tenth if needed.
1)
2)
)
4)
the bases on a baseball diamond are 90 feet apart. how far is it from home plate to second base (going straight across)?

1. an 18 - foot ladder is leaned against a wall. if the bottom of the ladder is 8 feet from the wall, how high up on the wall will the ladder reach?

Explanation:

Problem 1:

Step1: Identify legs and hypotenuse

We have a right triangle with legs \( a = 10\) m and \( b = 6\) m. We need to find the hypotenuse \( c \). The Pythagorean theorem is \( c=\sqrt{a^{2}+b^{2}}\).

Step2: Substitute values

Substitute \( a = 10\) and \( b = 6\) into the formula: \( c=\sqrt{10^{2}+6^{2}}=\sqrt{100 + 36}=\sqrt{136}\approx11.7\) m.

Step1: Identify legs and hypotenuse

We have a right triangle with legs \( a = 7\) m and hypotenuse \( c = 12\) m. We need to find the other leg \( b \). The Pythagorean theorem is \( b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \( a = 7\) and \( c = 12\) into the formula: \( b=\sqrt{12^{2}-7^{2}}=\sqrt{144 - 49}=\sqrt{95}\approx9.7\) m.

Step1: Identify legs and hypotenuse

We have a right triangle with legs \( a = 8\) m and hypotenuse \( c = 13\) m. We need to find the other leg \( b \). The Pythagorean theorem is \( b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \( a = 8\) and \( c = 13\) into the formula: \( b=\sqrt{13^{2}-8^{2}}=\sqrt{169 - 64}=\sqrt{105}\approx10.2\) m.

Answer:

\( \approx11.7\) m

Problem 2: