![\"art&pp2_img1\"](\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/artpp2_img1.png\")
<\/p>\nif you\u2019ve read part 1 of the \u201cconquering right triangles…\u201d series, you\u2019re ready to rock some more challenging act math questions with a quick \u201ctriangles\u201d quiz! try each question on your own, then check your answer against the explanation!<\/p>\n
question #1<\/b>: a right triangle with one length of 60 degrees has two leg lengths of x of and 2\u221a3. if side 2\u221a3 is across from the 60-degree angle, what is the measurement of x?<\/p>\n
a) 2<\/p>\n
b) 2\u221a3<\/p>\n
c) 4<\/p>\n
d) 4\u221a2<\/p>\n
e) 4\u221a3<\/p>\n
here it is a good example of how drawing the triangle can be vital to getting the correct answer on a right triangle question. a 30-60-90 triangle has a ratio of x: x\u221a3: 2x. if 2\u221a3 is across from the 60-degree angle, then x = 2. the correct answer is (a).<\/p>\n
question #2:<\/b> if triangle abc is a 30-60-90 right triangle, which of the following sets could represent triangle abc\u2019s side lengths?<\/p>\n
a) 2, 2, 2<\/p>\n
b) 2, 2, 2\u221a2<\/p>\n
c) 2, 2\u221a2, 2\u221a2<\/p>\n
d) 2, 2\u221a2, 2\u221a3<\/p>\n
e) 2, 2\u221a3, 4<\/p>\n
for each answer choice x = 2, so knowing that the ratio of a 30-60-90 is x: x\u221a3 : 2x<\/b>, we can plug x in to get: 2: 2\u221a3 : 2(2) or 2: 2\u221a3 : 4. the answer is (e).<\/p>\n
now let\u2019s look at an example with the 45-45-90 triangle:<\/p>\n
question #3:<\/b> which of the following sets of three numbers could be the side lengths, in yards, of a right triangle containing a 45\u00b0 angle?<\/p>\n
<\/p>\n
recall that a fractional exponent is just another way of expressing a root. we know the ratio for a 45-45-90 is x: x: x\u221a2<\/b>, which means two of the sides must be equal. that eliminates d and e. out of the remaining choices, only (c) correctly expresses the ratio.<\/p>\n
sometimes the act math test will make triangles more challenging by disguising them within larger figures. let\u2019s look at an example for our final practice problem!<\/p>\n
![\"art&pp2_img2\"](\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/artpp2_img2.png\")
<\/p>\n
question #4:\u00a0<\/b>what is the area of the trapezoid\u00a0in the figure provided?<\/b><\/p>\n
(a) 210<\/p>\n
(b) 360<\/p>\n
(c) 440<\/p>\n
(d) 570<\/p>\n
(e) 620<\/p>\n
the trapezoid consists of two smaller shapes: a triangle and a rectangle. draw a line from point a across this figure to form the two shapes.\u00a0 find the area of each shape and then add them together to find the area of the trapezoid.\u00a0 area of rectangle = length x width. therefore, the area of the rectangle is 18×20 = 360<\/p>\n
![\"art&pp2_img4\"](\"\/\/www.catharsisit.com\/act\/files\/2014\/02\/artpp2_img4.png\")
<\/p>\n
therefore, area of the triangle = (1<\/sup>\/2<\/sub>)(20)(21) = 210.\u00a0 the total area of the trapezoid = 360+210 = 570, or (d).<\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" if you\u2019ve read part 1 of the \u201cconquering right triangles…\u201d series, you\u2019re ready to rock some more challenging act math questions with a quick \u201ctriangles\u201d quiz! try each question on your own, then check your answer against the explanation! question #1: a right triangle with one length of 60 degrees has two leg lengths of […]<\/p>\n","protected":false},"author":97,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[8,9,13,6],"ppma_author":[24879],"acf":[],"yoast_head":"\n