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-Dominant- [34]
3 years ago
11

The area of triangle ABC is _____. A 60 B65 C130 D150

Mathematics
1 answer:
Romashka [77]3 years ago
7 0
Is there a picture that goes with the question ?
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The vertices of a triangle ABC are A(7, 5), B(4, 2), and C(9, 2). What is measure of angle ABC? 30° 45° 56.31° 78.69°
GenaCL600 [577]

The measure of angle ABC is 45°

<em><u>Explanation</u></em>

Vertices of the triangle are:   A(7, 5), B(4, 2), and C(9, 2)

According to the diagram below....

Length of the side BC (a) =\sqrt{(4-9)^2+(2-2)^2}= \sqrt{25}= 5

Length of the side AC (b) = \sqrt{(7-9)^2 +(5-2)^2}= \sqrt{4+9}=\sqrt{13}

Length of the side AB (c) = \sqrt{(7-4)^2 +(5-2)^2} =\sqrt{9+9}=\sqrt{18}

We need to find ∠ABC or ∠B . So using <u>Cosine rule</u>, we will get...

cosB= \frac{a^2+c^2-b^2}{2ac} \\ \\ cos B= \frac{(5)^2+(\sqrt{18})^2-(\sqrt{13})^2}{2*5*\sqrt{18} }\\ \\ cosB= \frac{25+18-13}{10\sqrt{18}} =\frac{30}{10\sqrt{18}}=\frac{3}{\sqrt{18}}\\ \\ cosB=\frac{3}{3\sqrt{2}} =\frac{1}{\sqrt{2}}\\ \\ B= cos^-^1(\frac{1}{\sqrt{2}})= 45 degree

So, the measure of angle ABC is 45°

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A _______ represents the idea of "if and only if." Its symbol is a double arrow, left right arrow↔.
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A <u>bi-conditional statement</u> represents the idea of "if and only if." Its symbol is a \leftrightarrow.

Step-by-step explanation:

We have been given an incomplete sentence. We are supposed to fill in the given blank.

A _______ represents the idea of "if and only if." Its symbol is a \leftrightarrow.

We know that "if and only if" stands for bi-conditional statement, which represents either both statements are true or both are false.

The symbol \leftrightarrow represent a bi-conditional statement.

Therefore, our complete statement would be: A <u>bi-conditional statement</u> represents the idea of "if and only if." Its symbol is a \leftrightarrow.

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