Q1. sin27° = x/8
Solution:
We have to solve for x, therefore, we will rearrange the given equation for x.
We get,
x = 8 × sin27°
Using the calculator,
sin27° = 0.45
Now substitute the value of sin27° into the main equation.
we get,
x = 8 × 0.45
x = 3.63 (rounded to the nearest hundredth)
Q2. tan 18° = n / 75
Solution:
We have to solve for n, therefore, we will rearrange the given equation for n.
We get,
n = 75 × tan 18°
Using the calculator,
tan 18° = 0.32
Now substitute the value of tan 18° into the main equation.
we get,
x = 75 × 0.32
x = 24.37 (rounded to the nearest hundredth)
Q3. sin40° = 4 / a
Solution: We have to solve for a, therefore, we will rearrange the given equation for a.
We get,
a = 4 ÷ sin40°
Using the calculator,
sin40° = 0.64
Now substitute the value of sin40° into the main equation.
we get,
a = 4 ÷ 0.64
a = 6.25 (rounded to the nearest hundredth)
Q4. cos5° = 92 / y
Solution: We have to solve for y, therefore, we will rearrange the given equation for y.
We get,
y = 92 ÷ cos5°
Using the calculator,
Cos5° = 0.99
Now substitute the value of cos5° into the main equation.
we get,
y = 92 ÷ 0.99
y = 92.92 (rounded to the nearest hundredth)
Q5: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 35°
length of Opposite side to the angle = x
Length of Hypoteneus = 12
Calculations:
Using the SOH CAH TOA rules:
SOH stands for SineФ = Opposite ÷ Hypotenuse.
CAH stands for CosineФ = Adjacent ÷ Hypotenuse.
TOA stands for TangentФ = Opposite ÷ Adjacent.
Hence,
SineФ = Opposite ÷ Hypotenuse
Substituting the values:
Sine35° = x ÷ 12
0.5735 = x ÷ 12
x = 0.5735 × 12
x = 6.88 (rounded to the nearest hundredth)
Q6: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = x
Length of Hypoteneus = 30
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Cos54° = x ÷ 30
0.5877 = x ÷ 30
x = 0.5877 × 30
x = 17.63 (rounded to the nearest hundredth)
Q7: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = 85
length of the opposite side to the angle = x
Calculations:
Using the SOH CAH TOA rules:
Hence,
TangentФ = Opposite ÷ Adjacent
Substituting the values:
tan22° = x ÷ 85
0.4040 = x ÷ 85
x = 0.4040 × 85
x = 34.34 (rounded to the nearest hundredth)
Q8: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 16°
length of the opposite side to the angle = x
Length of Hypoteneus = 14
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Sine16° = x ÷ 14
0.2756 = x ÷ 14
x = 0.2756 × 14
x = 3.86 (rounded to the nearest hundredth)
Q9: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = 9
length of the opposite side to the angle = x
Calculations:
Using the SOH CAH TOA rules:
Hence,
TangentФ = Opposite ÷ Adjacent
Substituting the values:
tan65° = x ÷ 9
2.1445 = x ÷ 9
x = 2.1445 × 9
x = 19.30 (rounded to the nearest hundredth)
Q10: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 51°
length of the adjacent side to the angle = x
Length of Hypoteneus = 70
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Cos51° = x ÷ 70
0.6293 = x ÷ 70
x = 0.6293 × 70
x = 44.05 (rounded to the nearest hundredth)
Q11: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 36°
length of the opposite side to the angle = 15
Length of Hypoteneus = x
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Sine36° = 15 ÷ x
0.5877 = 15 ÷ x
x = 15 ÷ 0.5877
x = 25.52 (rounded to the nearest hundredth)
Q12: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = x
length of the opposite side to the angle = 100
Calculations:
Using the SOH CAH TOA rules:
Hence,
TangentФ = Opposite ÷ Adjacent
Substituting the values:
tan65° = 100 ÷ x
2.1445 = 100 ÷ x
x = 100 ÷ 2.1445
x = 46.63 (rounded to the nearest hundredth)
Q13: When a 25-ft ladder is leaned against a wall, it makes a 72° with the ground. How high up on wall does the ladder reach?
The angle of elevation from the ground = 72°
length of the wall opposite to the angle = X
Length of ladder (Hypoteneus) = 25 feet
Calculations:
Using the SOH CAH TOA rules:
Hence,
SineФ = Opposite ÷ Hypotenuse
Substituting the values:
Sine72° = x ÷ 25
0.9510 = x ÷ 25
x = 25 ÷ 0.9510
x = 23.77 (rounded to the nearest hundredth)
ANSWERS TO QUESTION 14 AND 15 ARE ATTACHED
