The three right triangles below are similar.
The acute angles ∠C, ∠F, and ∠Z are all approximately measured to be 50.7°.
The side lengths for each triangle are as follows.
Note that the triangles are not drawn to scale.
A
C
B
9.8cm
11.97cm
15.47cm
50.7°
D
F
E
39.2cm
47.88cm
61.88cm
50.7°
X
Z
Y
58.8cm
71.82cm
92.82cm
50.7°
(a)For each triangle, find the ratio of the length of the side opposite 50.7° to the length of the hypotenuse. Round your answers to the nearest hundredth.
=ABAC =DEDF =XYXZ
(b)Use the ALEKS Calculator to find sin50.7°, cos50.7°, and tan50.7°.
Round your answers to the nearest hundredth.
=sin50.7° =cos50.7° =tan50.7°
(c)Which trigonometric function gives each ratio of sides in part (a)?
sine
cosine
tangent
none of these