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3 years ago

Find the following angle measures. mEAD = ° mCAB = °

Mathematics

2 answers:

Dimas [21]3 years ago

8 0

29 and 119
Just did it :(

sergejj [24]3 years ago

6 0

Part 1) Find m∠EAD

we know that

m∠EAD+m∠DAF+m∠BAF= $180\°$ ----> by supplementary angles

solve for m∠EAD

m∠EAD= $180\°$ -(m∠DAF+m∠BAF)

in this problem we have

m∠DAF= $90\°$

m∠BAF= $61\°$

substitute in the formula above

m∠EAD= $180\°-90\°-61\°=29\°$

therefore

the answer part 1) is

m∠EAD= $29\°$

Part 2) Find m∠CAB

we know that

m∠CAB+m∠BAF= $180\°$ --------> by supplementary angles

solve for m∠CAB

m∠CAB= $180\°$ -m∠BAF

in this problem we have

m∠BAF= $61\°$

substitute in the formula above

m∠CAB= $180\°-61\°=119\°$

therefore

the answer part 2) is

m∠CAB= $119\°$

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Proved

Step-by-step explanation:

Required

Prove that:

$(x\ sin\ a + y\ cos\ a)^2 + (x\ cos\ a - y\ sin\ a)^2 = x^2 + y^2$

Solving from left to right:

Open brackets

$(x\ sin\ a + y\ cos\ a)(x\ sin\ a + y\ cos\ a) + (x\ cos\ a - y\ sin\ a)(x\ cos\ a - y\ sin\ a) = x^2 + y^2$ $x^2\ sin^2 a + 2xy\ sin\ a\ cos\ a + y^2\ cos^2 a + x^2\ cos^2 a - 2xy\ sin\ a\ cos\ a + y^2\ sin^2 a = x^2 + y^2$

Collect Like Terms

$x^2\ sin^2 a + 2xy\ sin\ a\ cos\ a - 2xy\ sin\ a\ cos\ a + y^2\ cos^2 a + x^2\ cos^2 a+ y^2\ sin^2 a = x^2 + y^2$

$x^2\ sin^2 a + y^2\ cos^2 a + x^2\ cos^2 a+ y^2\ sin^2 a = x^2 + y^2$

Collect Like Terms

$x^2\ sin^2 a + y^2\ sin^2 a + x^2\ cos^2 a + y^2\ cos^2 a = x^2 + y^2$

Factorize:

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Further factorize

$(x^2 + y^2)(sin^2 a + cos^2 a) = x^2 + y^2$

In trigonometry:

$sin^2 a + cos^2 a = 1$

So, we have:

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