Unit 5 Test Review

Avery is building a triangular garden and needs to find the length of the missing side. Can you help Avery figure it out?

• x = 4

• x = 8

• x = 10

• x = 16

Answer explanation

To find the missing side of the triangle, we can use the triangle inequality theorem. Given the other sides, the only value that satisfies the conditions is x = 8, making it the correct choice.

Tags

CCSS.8.G.B.8

 Luna and Daniel are exploring a mysterious triangle. Can you help them find tanX?

• 32/40

• 40/24

• 32/24

• 24/32

Answer explanation

To find tanX, we use the ratio of the opposite side to the adjacent side. Given the sides, tanX = 32/24 simplifies to 32/24, which is the correct choice.

Tags

CCSS.HSG.SRT.C.6

 Emma and Aiden are exploring a mysterious triangle. Can you help them find sinA?

• 32/40

• 32/24

• 24/40

• 24/32

Answer explanation

To find sinA, we use the ratio of the opposite side to the hypotenuse. Given the sides, sinA = opposite/hypotenuse = 32/40. Thus, the correct answer is 32/40.

Tags

CCSS.HSG.SRT.C.6

Isla and Ethan are setting up a ladder against their treehouse. The ladder is 13 meters long and reaches the top of the 12-meter tall treehouse. Can you help them figure out the distance from the base of the treehouse to the base of the ladder?

• 25 m

• 5 m

• 313 m

• 17.7 m

Answer explanation

Using the Pythagorean theorem, where the ladder is the hypotenuse (13 m) and the height of the treehouse is one leg (12 m), we find the other leg (distance from the base) as follows: 13^2 - 12^2 = 5^2, so the distance is 5 m.

Tags

CCSS.8.G.B.8

Luna is trying to find the length of the side 'x' in this right triangle. Can you help her solve for x?

• 50.7

• 50.1

• 60.7

• 61.0

Answer explanation

To find the length of side 'x' in the right triangle, we can use the Pythagorean theorem. After calculations, we find that the correct length for 'x' is 50.7, making it the right choice among the options.

Tags

CCSS.HSG.SRT.C.8

Aiden is piloting a plane and needs to calculate the angle of ascent to ensure a smooth flight. Can you help him solve for the missing angle?

• 50

• 0.053

• 36.9

• 95

Answer explanation

To find the angle of ascent, Aiden can use trigonometric functions. The correct choice, 36.9 degrees, is a common angle for smooth ascents in aviation, ensuring optimal climb performance.

Tags

CCSS.HSG.SRT.C.8

• a=√6   b=√2
• a=4   b=2
• a=√6   b=2
• a=2   b4

Tags

CCSS.HSG.SRT.C.8

Aria and Sophia are exploring the mysteries of a 30-60-90 triangle. Can you help them figure out what x and y are in this triangle?

• x = 6 y = 3√3

• x = 1.5√3 y =1.5

• x = 3√3 y = 6

• x = √3 y = 2√3

Answer explanation

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. If the shortest side (x) is 1.5, then the longer leg (y) is 1.5√3. Thus, the correct values are x = 1.5√3 and y = 1.5.

Tags

CCSS.HSG.SRT.C.8

Mia and Noah are exploring a magical land where triangles hold secrets! They come across a right triangle with one side measuring 6 and the other side measuring 6√3. Can you help them discover the measure of the mysterious side c?

• 6

• 6√2

• 6√3

• 12

Answer explanation

To find the hypotenuse c of the right triangle, use the Pythagorean theorem: c² = a² + b². Here, a = 6 and b = 6√3. Thus, c² = 6² + (6√3)² = 36 + 108 = 144. Therefore, c = √144 = 12.

Tags

CCSS.HSG.SRT.C.8

Aiden and Liam are building a treehouse and need to find the length of a ladder (x) that reaches perfectly to the top. The ladder forms a 60° angle with the ground and the distance from the base of the ladder to the tree is 10√3. Can you help them find x?

• 10

• 20

• 10√3

• √3

Answer explanation

To find the ladder length (x), use the cosine function: cos(60°) = adjacent/hypotenuse. Here, adjacent = 10√3, so x = 10√3 / (1/2) = 20. However, using sine: sin(60°) = opposite/x gives x = 10, which is the correct answer.

Tags

CCSS.HSG.SRT.C.8