So I attached a diagram that illustrates the triangle that is formed. We know an angle, as well as the hypotenuse. We are looking for the height, or in other words the opposite side of the angle. There is a trigonometric function defined as: $sin(\theta) = \frac{opposite}{hypotenuse}$ . Using this we can plug in known values and solve for the opposite side, which I'll simply represent as x.

$sin(46) = \frac{x}{80}$

Multiply both sides by 80

$sin(46) * 80 = x$

Calculate sin(46) using a calculator (make sure it's in degree mode)

$0.7193398 * 80 = x$

Simplify

$57.547 \approx x$

Round this to the nearest foot

$58 \approx x$

4 0

1 year ago

The proof ABC ≅ DCB that is shown.

Schach [20]

The <em><u>correct answer</u></em> is:

AAS

Explanation:

AAS stands for "angle-angle-side." This states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

In these triangles, we have ∠CAB ≅ ∠CDB given to us to begin with. Throughout the proof, we find that ∠ABC ≅ ∠DCB. We also have that CB is congruent to itself. This is two angles and a side not included, so this is AAS.

4 0

2 years ago

Read 2 more answers

Graphing linear equations

ella [17]

Answer:

To ensure uniformity on an exam

To test whether you can distinguish between the two formats

Step-by-step explanation:

Standard form is when a straight line equation is rearranged in the form:

$ax + by = c$

Therefore y=2x+4 in standard form is

$2x - y = - 4$

The slope-intercept form is when a a straight line equation is written in the form:

$y = mx + c$

where m is the slope and c is the y-intercept.

The given equation is

$y = - \frac{1}{2} x - 5$

This is already in slope-intercept form:

The standard form and slope-intercept forms are just formats.

Your instructor may restrict you to leave your answer in one of these formats maybe for uniformity on a test.

You may also decide to rewrite an equation in slope-intercept form, so that you can easily identify the slope and y-intercept easily for graphing purpose.

6 0

3 years ago

Calculate the volume of this regular solid.

IgorC [24]

Answer:

V= 42.41

Step-by-step explanation:

$V = \pi r^{2}\frac{h}{3}$