SME
Grade 10 Math · Problem type
Find a side from an angle
Use this for “A 7.5 m ladder leans at 38° to the ground. How high up the wall does it reach?”
Diagram
sin A = o/h = 4.6175/7.5 ≈ 0.6157
cos A = b/h = 5.9101/7.5 ≈ 0.788
tan A = o/b
tan A = 4.6175/5.9101 ≈ 0.7813
This is an example. Type your own values to start a new problem.
sin(
A
°)
=
o
h
b
Foot from the wall
calculated
Formulas
sin(
A
°)
=
o
h
sin(38°)
=
4.6175
7.5
cos(
A
°)
=
b
h
cos(38°)
=
5.9101
7.5
o
2
+
b
2
=
h
2
4.6175
2
+
5.9101
2
=
7.5
2
Assumptions
•
The wall is straight up from level ground, so the right angle is at its foot.
•
The ladder is the hypotenuse; the height is opposite the angle A, the foot distance adjacent.
•
Multiply the hypotenuse by sin A for the opposite side, by cos A for the adjacent side.
Step-by-step
WE KNOW
A = 38°, h = 7.5 m
FIND
height up the wall (o), foot from the wall (b)
Step 1 · Find height up the wall (o)
Use sin(A°) = o ÷ h
Opposite
=
hypotenuse
×
sin
A
.
o
=
h
×
sin(
A
°)
o
=
7.5
×
sin(38°)
o
=
7.5
×
0.6157
o
=
4.6175
m
Step 2 · Find foot from the wall (b)
Use cos(A°) = b ÷ h
Adjacent
=
hypotenuse
×
cos
A
.
b
=
h
×
cos(
A
°)
b
=
7.5
×
cos(38°)
b
=
7.5
×
0.788
b
=
5.9101
m
Check
Put the numbers back in. Both sides should match.
sin(38°)
=
4.6175
7.5
✓
cos(38°)
=
5.9101
7.5
✓
4.6175
2
+
5.9101
2
=
7.5
2
✓
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