Find the measure of ∠M.

Mathematics

2 answers:

slamgirl [31]3 years ago

7 0

Answer:

36 degrees

Step-by-step explanation:

babunello [35]3 years ago

5 0

Answer:

180-84-60= 36 degrees

Step-by-step explanation:

a triangle is composed of 3 angles up to 180 degrees 180-84 is 96 96-60 is 36.

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If t a n squared θ = 3 /8 , what is the value of s e c θ

TEA [102]

We can use 3 facts:

$\tan{\theta}=\frac{y}{x}$

$\sec{\theta}=\frac{r}{x}$

$x^2+y^2=r^2$

So, to find our x and our y we can do:

$\tan^2{\theta}=\frac{3}{8} \implies \\ \tan{\theta}=\pm{\sqrt{\frac{3}{8}}=\pm\frac{\sqrt{3}}{\sqrt{8}}$ So, now that we know our x and our y we can find our r.

$(\sqrt{3})^2+(\sqrt{8})^2=11 \implies r=\sqrt{11}$

You'll notice, though, that there were two solutions for $\tan{\theta}$ , which means we have a positive and a negative for our x. So:

$\sec{\theta}=\frac{\sqrt{11}}{\sqrt{8}} \\ \sec{\theta}=-\frac{\sqrt{11}}{\sqrt{8}}}\\ \text{Rationalizing both of them:}\\ \sec{\theta}=\frac{\sqrt{88}}{8} \\ \sec{\theta}=-\frac{\sqrt{88}}{8}$