Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
5. Indirect Proof and Inequalities in One Triangle
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Exercise 35 Page 341

Practice makes perfect
a By the Triangle Sum Theorem, we can determine the remaining angles in △ BCA and △ BDA:
m∠ ABC+90^(∘)+40^(∘)=180^(∘) ⇒ m∠ ABC=50^(∘) m∠ ABD+90^(∘)+50^(∘)=180^(∘) ⇒ m∠ ABC=40^(∘)

Let's add these angle measures to the diagram.

Now we can use the Triangle Larger Angle Theorem to box in the width of the river, AB. Since m∠ Cm∠ ABD, the length of AB has to be greater than 35 yd.

b Any right triangle will be isosceles if one of the acute angles in the triangle is 45^(∘). Therefore, if we can measure an angle of 45^(∘) from C or D, then AC and DA will be the same length as the distance across the river, AB.