SME
Grade 10 Math · Problem type
Angle of elevation
Use this for “Standing 36 m from a tree, you look up 28° to its top. How tall is the tree?”
Diagram
sin A = u/c
sin A = 19.1415/40.77 ≈ 0.4695
cos A = d/c = 36/40.77 ≈ 0.8829
tan A = u/d = 19.1415/36 ≈ 0.5317
The top is 19.1415 above the eye, so 20.64 above the ground (19.1415 + 1.5).
This is an example. Type your own values to start a new problem.
tan(
A
°)
=
u (m)
d (m)
H (m)
=
u (m)
+
e (m)
Formulas
tan(
A
°)
=
u
d
tan(28°)
=
19.1415
36
H
=
u
+
e
20.6415 = 19.1415 + 1.5
Assumptions
•
The angle of elevation is measured up from a level line through the eye.
•
The height above the eye is opposite the angle: distance × tan A.
•
Add the eye height for the whole height; use 0 when the angle is measured at the ground.
•
An angle of depression, down from a level line, equals the angle of elevation back up.
Step-by-step
WE KNOW
d = 36 m, A = 28°, e = 1.5 m
FIND
height above the eye (u), height of the top (H)
Step 1 · Find height above the eye (u)
Use tan(A°) = u ÷ d
Opposite
=
adjacent
×
tan
A
.
u
=
d
×
tan(
A
°)
u
=
36
×
tan(28°)
u
=
36
×
0.5317
u
=
19.1415
m
Step 2 · Find height of the top (H)
Use H = u + e
Add the eye height to the height above the eye.
H
=
19.1415
+
1.5
H
=
20.6415
m
Check
Put the numbers back in. Both sides should match.
tan(28°)
=
19.1415
36
✓
20.6415 = 19.1415 + 1.5 ✓
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Right-triangle trigonometry: sine, cosine and tangent
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Use this for “sin 28° is about 0.4695. Which cosine is equal to it?”