Unformatted text preview: 0.6, we’ve had some experience
solving right triangles. The following example reviews what we know.
Example 11.2.1. Given a right triangle with a hypotenuse of length 7 units and one leg of length
4 units, ﬁnd the length of the remaining side and the measures of the remaining angles. Express
the angles in decimal degrees, rounded to the nearest hundreth of a degree. c= 7 Solution. For deﬁnitiveness, we label the triangle below. β
To ﬁnd the length of the missing side a, we use the Pythagorean Theorem to get a2 + 42 = 72
which then yields a = 33 units. Now that all three sides of the triangle are known, there are
several ways we can ﬁnd α using the inverse trigonometric functions. To decrease the chances of
propagating error, however, we stick to using the data given to us in the problem. In this case, the
lengths 4 and 7 were given, so we want to relate these to α. According to Theorem 10.4, cos(α) = 4 .
Since α is an acute angle, α = arccos 4 radians. Converting to de...
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