Lucas is designing a flower garden in the shape of an isosceles right triangle. He has created a scale diagram. The lengths of the perpendicular sides in the scale diagram are 7 cm, and the hypotenuse of the real garden will be 3 m long. What is the area of the real garden?
A. 450 m^2
B. 2.25 m^2
C. 1033 m^2
D. 4.5 m^2
Leoislookingdown, from the roof of a building, at a dump truck that is parked on the road. The angle of depression to the front of the truck is 58°, and the building is 37 m tall. What is the distance between the base of the building and the front of the truck?
A. 41 m
B. 23 m
C. 59 m
D. 27 m
Steph is 117 cm tall, and her eyes are 106 cm off the ground. She is using her new binoculars to look at a bird that is perched in a tree.
The angle of elevation is 28°, and Stephanie is 25.0 m from the base of the tree. What is the height of the bird in the tree?
A. 13.3 m
B. 12.8 m
C. 23.1 m
D. 14.4 m
Greg and Kristen are on opposite ends of a zip line that crosses a gorge. Greg went across the gorge first, and he is now on a ledge that is 15 m above the bottom of the gorge. Kristen is at the top of a cliff that is 72 m above the bottom of the gorge. Jon is on the ground at the bottom of the gorge, below the zip line. He sees Kristen at a 65° angle of elevation and Greg at a 35° angle of elevation. What is the width of the gorge, to the nearest metre?
A. 165 m
B. 152 m
C. 55 m
D. 106 m
In \triangle ABC, \angle A = 56^o
, \angle B = 64^o
, and c = 6.0
cm. What is the length of side a
?
A. 5.7 cm
B. 6.3 cm
C. 0.5 cm
D. 0.96 cm
An isosceles triangle has sides that measure 4 cm, 10 cm, and 10 cm. What is the area of the triangle?
A. 38 cm^2
B. 10 cm^2
C. 25 cm^2
D. 20 cm^2
A cyclist travels 4.50 km directly south, and then turns and travels 6.80 km in the direction N60°W. What distance, and in what direction, will the cyclist need to travel to get back to her starting point?
A. 5.00 km, N59.5°E
B. 6.00 km, N79.5°E
C. 5.00 km, N49.5°E
D. 4.00 km, N29.5°E