We only need to find the heights of the 2 points on the flagpole and then subtract them. We have that AC and DC are related by the following trigonometric number: tan60=AC/DC. This is because ADC is a right triangle and AC is the opposite leg of the angle we know, while DC is the adjacent leg.
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Thus, we have calculated AC. The same remarks apply to the triangle BCD; However, now we get that tan30=BC/DC.
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Hence, the height of point B is 5 feet, while the height of point A is 15 feet. Their distance is 10 feet.
All 3 angles of a triangle must equal to 180. You can simply set up an equation to solve this and set it equal to 180.
Angle 1 - 50 + x
Angle 2 - x
Angle 3 - 2x -10
50+x+x+2x-10=180
4x+40=180
4x=140
x=35
Angle 1 = 50+35= 85
Angle 2 = 35
Angle 3 = 2(35) - 10 = 60
60+35+85=180
The measure of the ∠LQP is 120°
Step-by-step explanation:
The diagram of the question is as attached in the image.
LMNP is a square. We know that for a square all sides are equal and intersects at 90°
Hence, LM=MP=PN=LN
and ∠LMP= ∠MPN= ∠PNL= ∠NLM= 90°
Δ LMQ is an equilateral triangle
We know that for equilateral triangle all sides are equal and all angles are 60°
LM=LQ=QM=MP=PN=LN and
∠LQM= ∠QML= ∠MLQ= 60°
∠LQP= ∠LQM+ ∠MQP eq 1
In Δ MPQ
∠QPM=90° and ∠PMQ= 90°-60°=30°
Hence, ∠MQP= 180°-(90°+30°)=60°
Putting the value of ∠MQP and ∠LQM in equation 1
∠LQP= 60°+60°= 120°
Thus the measure of ∠LQP=120°
To show the negative of a square root, a negative sign would have to be placed outside the radical.
Answer: D. 100
Step-by-step explanation:
