3 years ago

In the diagram below, m A = 59°, m B = 55° and m C = 78°. Find m D.

Mathematics

1 answer:

masya89 [10]3 years ago

3 0

Answer:

D=36

Step-by-step explanation:

All angles of the triangle add up to 180. Subtract 180-59-55=66

Then the missing measurement is a vertical which means that E=66.

So then 180-78-66=36

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Please help im really confused<br><br> Which expression is equivalent to 4(7 + 8)?

Hatshy [7]

Answer:

With the answer choices:

A. 11 + 8

B. 11 + 12

C. 28 + 12

D. 28 + 32

The answer would be 28+32.

Step-by-step explanation:

Use the distributive law.

4 * 7 = 28

4 * 8 = 32

Hope this helps!

8 0

2 years ago

In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.

Irina-Kira [14]

Given the values of the three sides of the triangle, we can apply the Cosine Law to find the angles of the triangle. Recall that for we can express the value of c through the equation below.

$c^{2} = a^{2} + b^{2} - 2abcosC$

Rearranging this equation, we can find the value ∠C as shown below.

$\cos C = \frac{a^{2}+b^{2}-c^{2}}{2ab}$
$C = cos^{-1} (\frac{a^{2}+b^{2}-c^{2}}{2ab})$

We can apply the same reasoning for finding the value of ∠B as shown.

$B = cos^{-1} (\frac{a^{2}+c^{2}-b^{2}}{2ac})$

Plugging in the values of the sides (see image attached) from the given. It will now be straightforward to compute for ∠B and ∠C.

$C = cos^{-1} (\frac{22.5^{2}+18^{2}-13.6^{2}}{2(22.5)(18)})$
$C \approx 37.19$

$B = cos^{-1} (\frac{22.5^{2}+13.6^{2}-18^{2}}{2(22.5)(13.6)})$
$B \approx 53.13$

Answer: ∠C = 37.19° and ∠B = 53.13°