Question

1. in a 45 - 45 - 90 triangle where the legs are 2 units long, what

a (2sqrt{2})
b 4
c 2
d (2sqrt{3})
10 in a 30 - 60 - 90 triangle where the shortest leg is 2 units, w
a (2sqrt{2})
b 4
c 2
d (2sqrt{3})
11 sine =
a opposite / hypotenuse
b adjacent / hypotenuse
c opposite / adjacent
12 cosine =
a opposite / hypotenuse
b adjacent / hypotenuse
c opposite / adjacent
13 tangent =
a opposite / hypotenuse
b adjacent / hypotenuse
c opposite / adjacent

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, if the length of each leg is $a$, the length of the hypotenuse $c$ is given by $c = a\sqrt{2}$. Here $a = 2$, so $c=2\sqrt{2}$.

Step2: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 triangle, if the shortest leg (opposite the 30 - degree angle) has length $x$, the hypotenuse has length $2x$. Given $x = 2$, the hypotenuse is $2\times2=4$.

Step3: Recall sine definition

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step4: Recall cosine definition

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step5: Recall tangent definition

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Answer:

1. A. $2\sqrt{2}$
2. B. 4
3. A. opposite / hypotenuse
4. B. adjacent / hypotenuse
5. C. opposite / adjacent