Answer: option c.
Step-by-step explanation:
You need to remember the identity:
The inverse of the tangent function is arctangent. You need to use this to calculate the angle "R":
You know that you need to find the measure of "R" and (which is the opposite side) and
(which is the adjacent side), you can sustitute values into
Then, you get:
The <em>missing</em> angle of the <em>right</em> triangle ABC has a measure of 30°. (Correct answer: A)
<h3>How to find a missing angle by triangle properties</h3>
Triangles are <em>geometrical</em> figures formed by three sides and whose sum of <em>internal</em> angles equals 180°. There are two kind of triangles existing in this question: (i) <em>Right</em> triangles, (ii) <em>Isosceles</em> triangles.
<em>Right</em> triangles are triangles which one of its angles equals 90° and <em>isosceles</em> triangles are triangles which two of its sides have <em>equal</em> measures.
According to the statement, we know that triangle BQR is an <em>isosceles</em> triangle, whereas triangles ABC, ANB and NBC are <em>right</em> triangles. Based on the figure attached below, we have the following system of <em>linear</em> equations based on <em>right</em> triangles ABC and NBC:
<em>2 · x + 90 + θ = 180</em> (1)
<em>(90 - x) + 90 + θ = 180</em> (2)
By equalizing (1) and (2) we solve the system for <em>x</em>:
<em>2 · x = 90 - x</em>
<em>3 · x = 90</em>
<em>x = 30</em>
And by (1) we solve the system for <em>θ</em>:
<em>θ = 180 - 2 · x - 90</em>
<em>θ = 30</em>
<em />
The <em>missing</em> angle of the <em>right</em> triangle ABC has a measure of 30°. (Correct answer: A)
To learn more on right triangles, we kindly invite to check this verified question: brainly.com/question/6322314
Answer:
Length of diagonal of picture = 15.30 inches
Step-by-step explanation:
Given that:
Side lengths of picture frame = 12 inches by 9.5 inches
As the picture is rectangular, the diagonal will form hypotenuse of right angled triangle.
Using Pythagorean theorem;
a²+b²=c²
Putting the values in the theorem
Taking square root on both sides
Hence,
Length of diagonal of picture = 15.30 inches