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SOH-CAH-TOA! Have you heard the call of the trig function? Use them to navigate the trickier sides (and angles) of geometric shapes.

The mast in the above diagram is \(9\) meters high and a wire is stretched tight to form a straight line to the top of the mast at an angle of \(60^\circ.\) How long is the wire in meters?

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The length of \(\overline{AC}\) is 4 and the length of \(\overline{BC}\) is \(2\sqrt{2}\). What is the length of \(\overline{AB}\)?

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In the above diagram, the length of the shadow of the building is \(a=32\) meters and the end of the shadow forms an angle of \(60^\circ\) with the sun. What is the height of the building?

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A perfectly straight tree is struck by lightning and breaks at point \(A\). After falling, the tree forms a triangle with the ground at angle \(\angle ACB =30^\circ\) and the distance between the top and bottom of the tree is \( d =27\text{ m},\) as illustrated in the above diagram. What is the height of the tree before being struck by lightning?

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The mast in the above diagram is \(21\) meters high and a wire is stretched tight to form a straight line to the top of the mast at an angle of \(60^\circ.\) How long is the wire in meters?

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