Question

unit 2: full review (triangles)
total questions: 24
worksheet time: 21 mins
instructor name: derek theiss

1. the hypotenuse of a triangle is:

(a) a² + b² = c²
b) any side (you pick)
c) the shortest side (opposite the 30 degree angle)
d) the longest side in a right triangle that is also opposite the 90 degree angle)

1. define the term right angle

(a) when two angles in a triangle are 90 degrees
b) any angle less than 90 degrees
c) three angles in a right triangle
d) a 90 degree angle

1. the pythagorean theorem is

(a) a² + b² + c²
b) a + b = c
(c) a² + b² = c²
d) a = lw

1. determine the length of the missing side using the pythagorean theorem.

(a) 7
b) 23
c) 17
d) 8

Explanation:

Step1: Recall hypotenuse definition

The hypotenuse is the longest side in a right - triangle, opposite the 90 - degree angle. So for question 1, the answer is d.

Step2: Recall right - angle definition

A right - angle is an angle that measures 90 degrees. So for question 2, the answer is d.

Step3: Recall Pythagorean Theorem

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\) for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\). So for question 3, the answer is c.

Step4: Apply Pythagorean Theorem

Let the missing side be \(x\). If the hypotenuse \(c\) is unknown and the legs are \(a = 8\) and \(b=15\), by the Pythagorean Theorem \(c=\sqrt{a^{2}+b^{2}}=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17\). So for question 4, the answer is c.

Answer:

1. d. The longest side in a right triangle that is also opposite the 90 degree angle
2. d. A 90 degree angle
3. c. \(a^{2}+b^{2}=c^{2}\)
4. c. 17