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Math Help - Needing help with angle of evaluation

  1. #1
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    Needing help with angle of evaluation

    Please help me to answer these questions:

    (a) When the angel of elevation of the sun is 62 degrees, the shadow cast by a vertical pole is 10m long. Find the height of the pole correct to one decimal place.

    (b) If a=8, c=5 and A=72 degrees, find the size of the angle C?

    (c) A ladder is 7m long and reaches 5m up a vertical wall. Find the angle between the ladder and the horizontal.

    (d) Find the area of the triangle shown in the diagram:Needing help with angle of evaluation-2012-04-28-16.50.21.jpg

    Thanks a million!
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  2. #2
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    Re: Needing help with angle of evaluation

    Quote Originally Posted by Molly1313 View Post
    Please help me to answer these questions:

    (a) When the angel of elevation of the sun is 62 degrees, the shadow cast by a vertical pole is 10m long. Find the height of the pole correct to one decimal place.

    make a sketch ... use the tangent ratio

    (b) If a=8, c=5 and A=72 degrees, find the size of the angle C?

    make a sketch ... use the law of sines

    (c) A ladder is 7m long and reaches 5m up a vertical wall. Find the angle between the ladder and the horizontal.

    make a sketch ... use the sine ratio.

    (d) Find the area of the triangle shown in the diagram:Click image for larger version. 

Name:	2012-04-28 16.50.21.jpg 
Views:	3 
Size:	720.6 KB 
ID:	23724

    if 8 is the base of the triangle, then the height of the triangle is 6sin(52)
    ...
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  3. #3
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    Re: Needing help with angle of evaluation

    Quote Originally Posted by Molly1313 View Post
    Please help me to answer these questions:

    (a) When the angel of elevation of the sun is 62 degrees, the shadow cast by a vertical pole is 10m long. Find the height of the pole correct to one decimal place.
    Draw a sketch! You are dealing with a right triangle. Use the tan-function: \tan(62^\circ) = \frac{length\ of\ pole}{10\ m}

    (b) If a=8, c=5 and A=72 degrees, find the size of the angle C?
    Draw a sketch! Use the Sine-rule.

    (c) A ladder is 7m long and reaches 5m up a vertical wall. Find the angle between the ladder and the horizontal.
    Draw a sketch! You are dealing with a right triangle whose hypotenuse is 7 m long. Use the Sine-function.

    (d) Find the area of the triangle shown in the diagram:Click image for larger version. 

Name:	2012-04-28 16.50.21.jpg 
Views:	3 
Size:	720.6 KB 
ID:	23724

    Thanks a million!
    The area of a triangle is calculated by:

    a = \frac12 \cdot 8\ cm \cdot h_{of\ the\ base}

    Draw the height of the base into your sketch. You are now dealing with a right triangle. Use the Sine-function: \sin(62^\circ)=\frac h6
    Solve for h. Plug in this term into the equation of the area.
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