1) Use Pythagorean Theorem to solve for the missing side length. Leave radical answers as radicals.
a) Given right \(\triangle WHO\) with \(m\angle W = 90^{\circ}\), \(WH = 5\) and \(WO = 12\), find \(HO\).
b) Given right \(\triangle SAW\)with \(m\angle A = 90^{\circ}\), \(SA = 4\) and \(SW = 5\), find \(AW\).
c) Given right \(\triangle THE\) with \(m\angle H = 90^{\circ}\), \(TH = 14\) and \(TE = 50\), find \(HE\).
d) Given right \(\triangle BIG\) with \(m\angle I = 90^{\circ}\), \(BI = 6\) and \(BG = 22\), find \(IG\).
e) Given right \(\triangle OWL\) with \(m\angle O = 90^{\circ}\), \(OL = 9\) and \(WL = 41\), find \(OW\).
f) Given right \(\triangle FLY\) with \(m\angle Y = 90^{\circ}\), \(FY = 6\) and \(LY = 9\), find \(FL\).
2): Use Pythagorean Triples to solve for the missing side length. Try to do the problems without using Pythagorean Theorem. You may need to look for common multiples of Pythagorean Triples to solve.
The first five Pythagorean Triples:
\(3, 4, 5\)
\(5, 12, 13\)
\(7, 24, 25\)
\(8, 15, 17\)
\(9, 40, 41\)
a) Given right \(\triangle WHY\) with \(m\angle W = 90^{\circ}\), \(WH = 3\) and \(WY = 4\), find \(HY\).
b) Given right \(\triangle NOT\) with \(m\angle N = 90^{\circ}\), \(NO = 4\) and \(NT = 7.5\), find \(OT\).
c) Given right \(\triangle TRY\) with \(m\angle T = 90^{\circ}\), \(TR = 25\) and \(RY = 65\), find \(TY\).
d) Given right \(\triangle THE\) with \(m\angle T = 90^{\circ}\), \(TH = 21\) and \(HE = 75\), find \(TE\).
e) Given right \(\triangle RED\) with \(m\angle R = 90^{\circ}\), \(RD = 3\) and \(ED = 5\), find \(RE\).
f) Given right \(\triangle ONE\) with \(m\angle O = 90^{\circ}\), \(OE = 80\) and \(NE = 82\), find \(ON\).
a) Given right \(\triangle WHO\) with \(m\angle W = 90^{\circ}\), \(WH = 5\) and \(WO = 12\), find \(HO\).
b) Given right \(\triangle SAW\)with \(m\angle A = 90^{\circ}\), \(SA = 4\) and \(SW = 5\), find \(AW\).
c) Given right \(\triangle THE\) with \(m\angle H = 90^{\circ}\), \(TH = 14\) and \(TE = 50\), find \(HE\).
d) Given right \(\triangle BIG\) with \(m\angle I = 90^{\circ}\), \(BI = 6\) and \(BG = 22\), find \(IG\).
e) Given right \(\triangle OWL\) with \(m\angle O = 90^{\circ}\), \(OL = 9\) and \(WL = 41\), find \(OW\).
f) Given right \(\triangle FLY\) with \(m\angle Y = 90^{\circ}\), \(FY = 6\) and \(LY = 9\), find \(FL\).
2): Use Pythagorean Triples to solve for the missing side length. Try to do the problems without using Pythagorean Theorem. You may need to look for common multiples of Pythagorean Triples to solve.
The first five Pythagorean Triples:
\(3, 4, 5\)
\(5, 12, 13\)
\(7, 24, 25\)
\(8, 15, 17\)
\(9, 40, 41\)
a) Given right \(\triangle WHY\) with \(m\angle W = 90^{\circ}\), \(WH = 3\) and \(WY = 4\), find \(HY\).
b) Given right \(\triangle NOT\) with \(m\angle N = 90^{\circ}\), \(NO = 4\) and \(NT = 7.5\), find \(OT\).
c) Given right \(\triangle TRY\) with \(m\angle T = 90^{\circ}\), \(TR = 25\) and \(RY = 65\), find \(TY\).
d) Given right \(\triangle THE\) with \(m\angle T = 90^{\circ}\), \(TH = 21\) and \(HE = 75\), find \(TE\).
e) Given right \(\triangle RED\) with \(m\angle R = 90^{\circ}\), \(RD = 3\) and \(ED = 5\), find \(RE\).
f) Given right \(\triangle ONE\) with \(m\angle O = 90^{\circ}\), \(OE = 80\) and \(NE = 82\), find \(ON\).
3) A boy is flying a kite in his yard and his kite gets stuck at the top of a tree. After pulling on the string hard enough to get his kite back, he realizes that he can now answer the question, “How tall is that tree?” What method does the boy use to find the height of the tree?
4) The string from his hand to the kite was \(42.3\) feet and he was standing \(32.2\) feet from the base of the tree. How tall is the tree (to the nearest tenth of a foot)? |
8) Use Pythagorean Converse to determine if given \(\triangle ABC\) is a right, acute, or obtuse. Remember to determine if the side lengths can form a triangle in the first place.
a) \(AB = 3\) and \(AC = 4\), \(BC = 5\)
b) \(AB = 4\) and \(AC = 8\), \(BC = 10\)
c) \(AB = 23\) and \(AC = 33\), \(BC = 63\)
d) \(AB = 39\) and \(AC = 27\), \(BC = 47\)
e) \(AB = 9\) and \(AC = 12\), \(BC = 16\)
a) \(AB = 3\) and \(AC = 4\), \(BC = 5\)
b) \(AB = 4\) and \(AC = 8\), \(BC = 10\)
c) \(AB = 23\) and \(AC = 33\), \(BC = 63\)
d) \(AB = 39\) and \(AC = 27\), \(BC = 47\)
e) \(AB = 9\) and \(AC = 12\), \(BC = 16\)
9) Given \(\triangle YET\), with \(YE = 8\) and \(YT = 5\)
a) Give two values for \(\overline{ET}\) that would make the triangle a right triangle.
b) Give the range of values for \(\overline{ET}\) that would make the three sides NOT form a triangle.
c) Give the range of values for \(\overline {ET}\) that would make the triangle an acute triangle.
d) Give the range of values for side \(\overline {ET}\) that would make the triangle an obtuse triangle.
a) Give two values for \(\overline{ET}\) that would make the triangle a right triangle.
b) Give the range of values for \(\overline{ET}\) that would make the three sides NOT form a triangle.
c) Give the range of values for \(\overline {ET}\) that would make the triangle an acute triangle.
d) Give the range of values for side \(\overline {ET}\) that would make the triangle an obtuse triangle.
11) \(\triangle ABE\) is formed when \(\overline {AE}\) and \(\overline {BE}\) are drawn. \(E\) is a point that can be anywhere on the red line (\(y = 6\) line).
a) For what two ordered pairs of point \(E\) make \(\triangle ABE\) a right triangle? b) For both of these answers, what would be the length of \(AE\) and \(BE\)? c) For what range of \(x\) coordinates of point \(E\) make \(\triangle ABE\) an acute triangle? d) What would the range of values of the length of \(\overline{AE}\) be for \(\triangle ABE\) to be an acute triangle? |
12) When a standard analog clock reads 12:00 pm (noon), both the hour and minute hands are pointing straight up and the angle formed by the hands is zero degrees. When the hands of the clock read exactly 5:43, do they form a right, acute or obtuse angle? Note that the hour hand moves \(0.5\) of a degree every passing minute and the minute hands moves 6 degrees every passing minute. Examine the angle "between" the hands. Justify your answer.
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Desmos or GeoGebra Challenge
Construct a triangle with movable vertex that illustrates the type of triangle based on angle measure.
Solution Bank
Construct a triangle with movable vertex that illustrates the type of triangle based on angle measure.
Solution Bank