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Mathematics

1 answer:

ollegr [7]2 years ago

7 0

Answer:

yes true I once made a post like this but the mods deleted it before I could put it up lol XD

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You need to find the distance across a river, so you make a triangle. BC is 661 feet, m∠B=103.2° and m∠C=14.4°. Find AB.

kati45 [8]

Answer:

AB = 185.77 feet

Step-by-step explanation:

From the figure attached, in ΔABC,

m∠B = 103.2°, m∠C = 14.4° and side BC = 661 feet

We have to find the measure of side AB.

Since ∠A + ∠B + ∠C = 180°

∠A + 103.2 + 14.4 = 180

∠A + 117.6 = 180

∠A = 180 - 117.6

= 62.4°

By applying sine rule in the given triangle ABC

$\frac{AB}{sinC}=\frac{BC}{sinA}$

$\frac{AB}{sin14.4}=\frac{661}{sin62.4}$

$\frac{AB}{0.249}=\frac{661}{0.886}$

AB = $\frac{0.249\times661}{0.886}$

= 185.77 feet

Therefore, AB = 185.77 feet will be the answer.

4 0

3 years ago

What is cos theta when sin theta = sqrt 2/3

Fittoniya [83]

Answer:

Value of cosθ is ±√7/3 .

Step-by-step explanation:

According to the Question , value of :

$\red{\implies sin\theta = \dfrac{\sqrt2}{3}}$

And , we know the identity of sine and cosine as ,

$\boxed{\pink{\sf\implies sin^2\theta + cos^2\theta = 1} }$

Using , this identity we have ;

$\implies sin^2\theta + cos^2\theta = 1 \\\\\implies \bigg( \dfrac{\sqrt2}{3}\bigg)^2 + cos^2\theta = 1 \\\\\implies \dfrac{2}{9} + cos^2\theta = 1 \\\\\implies cos^2\theta = 1 - \dfrac{2}{9} \\\\\implies cos^2\theta = \dfrac{9-2}{9} \\\\\implies cos\theta = \sqrt{\dfrac{7}{9}} \\\\\underline{\boxed{\blue{\bf \implies cos\theta = \pm \dfrac{\sqrt 7 }{3}}}}$