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nlexa [21]
3 years ago
7

URGENT PLEASE HELP!!!! GIVING BRAINLIEST!! If you answer this correctly ill answer some of your questions you have posted! (39pt

s)

Mathematics
1 answer:
Musya8 [376]3 years ago
8 0

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!

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