First of all, we have to observe this triangles separated by the height. These small and big triangles are similar according to the Angle-Angle-Angle principle.
a. We can find all of these length using the cosine of the angle, Pythagoras theorem and the principle of the similarity of triangles.
b. According to the cosine of the angle we can write that, cosθ = 12/a = 5/13 and from here a = 31.2. After finding that using Pythagoras theorem, we can write that 
. According to the similarity of the triangles, we can write that 31.2/d = 28.8/12 and d = 13. Applying Pythagoras theorem we find that c = 5.
c. We already gave the answer for this question in part b
Answer:
15/8
Step-by-step explanation:
Opp/Adj of angle x means Tan x
that would be 15/8
Answer:
<em>The measure of the angles is 45° and 135°</em>
Step-by-step explanation:
When two lines intersect, a linear pair of angles is formed. Two angles are said to be linear if they are adjacent, so a linear pair of angles must add up to 180 degrees.
Let's call x and y the two required angles. Knowing they form a linear pair:
x+y=180
We also know one angle is 1/3 of the other angle, thus:
x=y/3
Or, equivalently:
3x=y
Substituting y into the first equation:
x+3x=180
Simplifying:
4x=180
Solving:
x=180/4=45
The other angle is:
y=3x=3\cdot 45=135
Thus the measure of the angles is 45° and 135°
Answer:
A
Step-by-step explanation:
RT=12
TU=5
RU=12+5=17
RS=17+7=24
SU=√(RS²-RU²)=√(24²-17²)=√(24-17)(24+17)=√(7×41)=√287
area=1/2×12×√287=6×√287≈101.6 unit²
Answer:
x = 147 degrees
Step-by-step explanation:
The sum of angle x and 33 degrees must be 180 degrees. Thus, to find x, subtract 33 degrees from 180 degrees, obtaining 147 degrees.
