Mathematics, 26.07.2021 16:40 elizabethivy75

What is the value of x in the triangle?
15
30°
X
60°

Answers: 3

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Answers

Answer from: nunuskies

x = 7.5 $\sqrt{2}\\$

Step-by-step explanation:

Obviously, we can tell this is a right triangle, but to be more specific, it's a 30º-60º-90º triangle, meaning that one side is 90º, and the other two are 30 and 60 degrees.

When given a 30º-60º-90º triangle, you can solve the length of the other two sides even if only one side length is given. For a 30º-60º-90º triangle, the sides are given in x - x $\sqrt{2}\\$ - 2x form. The side opposite the 30º is always x (which is given in the picture you provided), the side opposite the 60º is always x $\sqrt{2}\\$ , and the side opposite the 90º is always 2x.

So the side opposite the 60º is 15, which is x $\sqrt{2}\\$ . We can write an equation:

15 = x $\sqrt{2}\\$

÷ $\sqrt{2}\\$ ÷ $\sqrt{2}\\$

$\frac{15}{\sqrt{2} }$ = x

Now we can't leave a number with a square root at the bottom, so we multiply both the numerator and the denominator by $\sqrt{2}\\$ .

$\frac{15\sqrt{2} }{2}$ = x

7.5 $\sqrt{2}\\$ = x

Answer from: Quest

In the first triangle 80+20+p=180 (since sum of all angles of a triangle is 180)so p= 80also in second triangle 55+45+q=180 (since sum of all angles of a triangle is 180)so q=80so we can conclude that p=80 degrees q=80 degrees so p=q=80 degreeshence option b is correct
What do you know to be true about the values of p and q?

What do you know to be true about the values of p and q?

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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What is the value of x in the triangle?
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60°
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