Special Right Triangles
Trigonometric Ratios
Finding Missing Sides and Angles
Angles of Elevation and Depression
100
Find the length of the legs.
x=4
100
Find sin(a) .
sin(a)=8/17
100
Find the side x (round to two decimal places).
x=12.14 cm
100
The distance from the base of a tree to a point of observation is 4.2 m. The angle of elevation from this point to the top of the tree is 38 degrees. What is the height of the tree (round to one decimal place)?
h=3.3 m
200
Find the length of the two legs.
x=9
y=9sqrt3
200
Find cos(t) and tan(t) .
cos(t)=56/65
tan(t)=33/56
200
Find the missing angle (round to two decimal places).
theta=33.75°
200
A ladder leans against a brick wall. The bottom of the ladder is 6 feet from the wall. The ladder reaches a height of 15 feet on the wall. Find to the nearest degree the angle the ladder makes with the wall.
x=22°
300
Find the length of the legs.
x=5sqrt2
300
Find tan(A) and sin(B).
tan(A)=3/4
sin(B)=4/5
300
Find the two missing sides and angle (round to two decimal places).
adjacent = 18.41 cm
opposite = 7.81 cm
angle = 67°
300
At a certain time of the day, a light post, 6 m tall, has a shadow of 5.8 m. If the angle of elevation of the sun at that time is θ°, find θ to two decimal places.
theta=45.97°
400
Find the lengths of the two remaining sides.
leg = 9
hypotenuse = 6sqrt3
400
Find tan(A) .
tan(A)=sqrt15/5
400
Find x (round to a whole number).
x=188
400
From the top of a rocky ledge 188 m high, the angle of depression to a boat is 13°. If the boat is d m from the foot of the cliff, find d correct to the nearest whole number.
d=814 m
500
Find x and y.
x=6
y=2sqrt3
500
Find cos(P) and sin(P).
cos(P)=sqrt190/19
sin(P)=(3sqrt19)/19
500
Find x (round to a whole number).
x=87
500
Two buildings with flat roofs are 80 feet apart. The shorter building is 55 feet tall. From the roof of the shorter building, the angle of elevation to the edge of the taller building is 32°. How high is the taller building (round to a whole number)?
h=105 ft