Answer:
ΔMNO= 90°, <em>m </em>= 7.316 cm, <em>n</em> = 16.69 cm
Step-by-step explanation:
The little square in the corner tells you that the angle is 90°
<u><em>Calculating the length of m</em></u>
We know that the Tangent of an angle is gotten by dividing the <u>opposite</u> side by the <u>adjacent</u> side, i.e,
Tan Ф = Opposite ÷ Adjacent
hence:
Tan 26° = <em>m </em>÷ 15
0.4877 = <em>m </em>/ 15
make <em>m </em>the subject and multiply both sides by 15
0.4877 × 15 = <em>m </em>/ 15 × 15
7.3155 = <em>m</em>
∴ <em>m </em>= 7.316 cm
<u><em>Calculating the length of n</em></u>
For this we can use the Pythagoras theorem that states, a² + b² = c² where <em>m </em>= <em>a</em><em>, </em><em>b </em>=<em> </em>15 cm and <em>c</em> = <em>n</em>. Hence:
7.316² + 15² = <em>c </em>²
53.52 + 225 = <em>c ²</em>
278·52 = <em>c ²</em>
<em>c</em> = √278·52
<em>c</em> = 16.69
∴ <em>n </em>= 16.69 cm
We could also use the Cosine of ΔOMN to get length <em>n </em>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 ÷ <em>n</em>
0.8987 = 15 / <em>n</em>
Make 15 the subject and multiply both sides by <em>n</em>
0.8987 × <em>n </em>= 15 / <em>n </em>× <em>n</em>
0.8987 <em>n </em>= 15
Divide both sides by 0.8987
0.8987 <em>n </em>÷ 0.8987 = 15 ÷ 0.8987
∴ <em>n </em>= 16.69 cm
Hope this helps!
If any of this does not make sense let me know and ill try to clarify better