Given: ∆ABC, AB = 8 m∠C = 90° m∠B = 40° Find: Perimeter of ∆ABC

Mathematics

2 answers:

iren [92.7K]3 years ago

6 0

Your answer is 19.270656422

first, you have that sin(40)=x/8, the leg opposite and the hypotenuse. the your x is 5.142300877. To find the other leg, you do tan(40) =x/5.142300877, which is the same thing as x= 5.14230087/tan(40). your x will be 6.128355545. the only thing to do is add up the sides, and you get 19.270656422]

Naddik [55]3 years ago

5 0

Answer:

The perimeter of the triangle ABC is 19,27 m

Step-by-step explanation:

In order to solve this we first have to create a triangle rectangle, check the image attached to understand it better, and with that we use law of sines in order to calculate the other sides of the triangle:

As you can see we know that the hypothenuse is 8 m, and we have both angles, so for the angle that is opposed to the 50º angle we will use 8cos50=5,1423 m.

For the side that is opposed to the 40º angle we will use 8cos40:6,1283m

SO to calculate the perimeter we just add the three sides:

5,1423 + 6,1283 + 8= 19,27

The perimeter of the triangle ABC is 19,27 m

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What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9

skelet666 [1.2K]

Answer:

Step-by-step explanation:

Let $u^2=x^4\\u = x^2$

Subbing in:

$9u^2-2u-7=0$

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:

$9u^2-9u+7u-7=0$

Group together in groups of 2:

$(9u^2-9u)+(7u-7)=0$

Now factor out what's common within each set of parenthesis:

$9u(u-1)+7(u-1)=0$

We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:

$(u-1)(9u+7)=0$

Remember that $u=x^2$

so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.

$(x^2-1)(9x^2+7)=0$

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring $(x^2-1)$ gives us that x = 1 and -1. The other set is a bit more tricky. If