Question

question 8: standard g.srt.8
solve for the missing side using the pythagorean theorem.
image of a right triangle with legs 5 and 2
a. 1.5
b. 5.4
c. 2.3
d. 3
question 9: standard g.srt.8
solve for the missing side using the pythagorean theorem.
image of a right triangle with hypotenuse 6.5 and one leg 2.7
a. 6.3
b. 4
c. 5.9
d. 10.2
question 10: standard g.srt.8
solve for the missing side using the pythagorean theorem.
image of a right triangle with hypotenuse 19 and one leg 17
a. 8.5
b. 9.2
c. 16.3
d. 10.3

Explanation:

Question 8

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, \(a\) and \(b\) are the legs. Here, \(a = 5\), \(b = 2\), find \(c\)? Wait, no, wait—wait, maybe I mixed up. Wait, the legs are 5 and 2? Wait, no, the right angle is between 5 and 2? Wait, no, the triangle has legs 5 and 2? Wait, no, the vertical leg is 5, horizontal leg is 2, so hypotenuse is \(c\). Wait, but the options are small. Wait, maybe I got the legs wrong. Wait, maybe the hypotenuse is 5, and one leg is 2, find the other leg. Oh! That makes sense. Because the options are around 5 or less. So let's correct: Let’s say hypotenuse \(c = 5\), one leg \(a = 2\), find the other leg \(b\). Then \(b=\sqrt{c^2 - a^2}\).

Step2: Calculate \(b\)

\(c = 5\), \(a = 2\), so \(b=\sqrt{5^2 - 2^2}=\sqrt{25 - 4}=\sqrt{21}\approx 4.58\)? Wait, no, the options are 1.5, 5.4, 2.3, 3. Wait, maybe the vertical leg is 5? No, wait the triangle: vertical side 5, horizontal side 2, right angle. So hypotenuse is \(\sqrt{5^2 + 2^2}=\sqrt{25 + 4}=\sqrt{29}\approx 5.385\), which is approximately 5.4. So that's option b.

Step1: Identify hypotenuse and leg

The triangle has hypotenuse 6.5, one leg 2.7, find the other leg \(b\). Using Pythagorean theorem: \(b=\sqrt{c^2 - a^2}\), where \(c = 6.5\), \(a = 2.7\).

Step2: Calculate \(b\)

\(c = 6.5\), \(a = 2.7\), so \(b=\sqrt{6.5^2 - 2.7^2}=\sqrt{42.25 - 7.29}=\sqrt{34.96}\approx 5.91\), which is approximately 5.9, option c.

Step1: Identify hypotenuse and leg

The triangle has hypotenuse 19, one leg 17, find the other leg \(b\). Using \(b=\sqrt{c^2 - a^2}\), where \(c = 19\), \(a = 17\).

Step2: Calculate \(b\)

\(c = 19\), \(a = 17\), so \(b=\sqrt{19^2 - 17^2}=\sqrt{(19 - 17)(19 + 17)}=\sqrt{2\times36}=\sqrt{72}\approx 8.485\), wait, but the options are 8.5, 9.2, 16.3, 10.3. Wait, 8.5 is option a. Wait, \(\sqrt{72}\approx 8.485\approx 8.5\), so option a.

Answer:

b. 5.4

Question 9