Answer:
ΔMNO= 90°, m = 7.316 cm, n = 16.69 cm
Step-by-step explanation:
The little square in the corner tells you that the angle is 90°
Calculating the length of m
We know that the Tangent of an angle is gotten by dividing the opposite side by the adjacent side, i.e,
Tan Ф = Opposite ÷ Adjacent
hence:
Tan 26° = m ÷ 15
0.4877 = m / 15
make m the subject and multiply both sides by 15
0.4877 × 15 = m / 15 × 15
7.3155 = m
∴ m = 7.316 cm
Calculating the length of n
For this we can use the Pythagoras theorem that states, a² + b² = c² where m = a, b = 15 cm and c = n. Hence:
7.316² + 15² = c ²
53.52 + 225 = c ²
278·52 = c ²
c = √278·52
c = 16.69
∴ n = 16.69 cm
We could also use the Cosine of ΔOMN to get length n i.e,
The Cosine of an angle is equal to the adjacent side divided by the hypotenuse.
Cosine Ф = Adjacent ÷ Hypotenuse
Cosine 26° = 15 cm ÷ n
0.8987 = 15 / n
Make 15 the subject and multiply both sides by n
0.8987 × n = 15 / n × n
0.8987 n = 15
Divide both sides by 0.8987
0.8987 n ÷ 0.8987 = 15 ÷ 0.8987
∴ n = 16.69 cm
Hope this helps!
