Difference between revisions of "1960 AHSME Problems/Problem 4"
Rockmanex3 (talk | contribs) (Solution to Problem 4) |
Rockmanex3 (talk | contribs) (Diagram for Problem 3) |
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==Solution== | ==Solution== | ||
If two of the angles are <math>60^{\circ}</math>, then the other angle is <math>60^{\circ}</math> because angles in triangle add up to <math>180^{\circ}</math>. That makes the triangle an equilateral triangle, so all sides are <math>4</math> inches long. | If two of the angles are <math>60^{\circ}</math>, then the other angle is <math>60^{\circ}</math> because angles in triangle add up to <math>180^{\circ}</math>. That makes the triangle an equilateral triangle, so all sides are <math>4</math> inches long. | ||
+ | |||
+ | ￼<asy> | ||
+ | draw((0,0)--(50,0)--(25,43.301)--cycle); | ||
+ | label("$4$",(10,25)); | ||
+ | label("$2$",(12.5,-5)); | ||
+ | label("$2$",(37.5,-5)); | ||
+ | label("$4$",(40,25)); | ||
+ | draw((25,43.301)--(25,0)); | ||
+ | label("$2\sqrt{3}$",(20,15)); | ||
+ | draw((25,3)--(28,3)--(28,0)); | ||
+ | </asy> | ||
Using the area formula <math>A = \frac{s^2\sqrt{3}}{4}</math>, the area of the triangle is <math>\frac{4^2\sqrt{3}}{4} = 4\sqrt{3}</math> square inches, which is answer choice <math>\boxed{\textbf{(C)}}</math>. | Using the area formula <math>A = \frac{s^2\sqrt{3}}{4}</math>, the area of the triangle is <math>\frac{4^2\sqrt{3}}{4} = 4\sqrt{3}</math> square inches, which is answer choice <math>\boxed{\textbf{(C)}}</math>. |
Revision as of 10:54, 8 May 2018
Problem
Each of two angles of a triangle is and the included side is inches. The area of the triangle, in square inches, is:
Solution
If two of the angles are , then the other angle is because angles in triangle add up to . That makes the triangle an equilateral triangle, so all sides are inches long.
￼
Using the area formula , the area of the triangle is square inches, which is answer choice .
See Also
1960 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |