A ladder is leaning against a building, forming a \( 70^{\circ} \) angle with the ground. The base of the ladder is 8.2 ft from the base of the building. What is the length of the ladder? Round your answer to the nearest tenth of a foot.

d) \( \frac{\sin \theta}{1-\cos \theta}-\frac{1+\cos \theta}{\sin \theta}=0 \quad \checkmark \checkmark \checkmark \checkmark \checkmark \)

3. Prove \( \sin 3 x=3 \cos ^{2} x \sin x-\sin ^{2} x \) 4. Prove \( \sec 2 x=\frac{\csc ^{2} x}{\csc ^{2} x-2} \) 5. Prove \( \frac{1+\cos \theta}{\sin \theta}+\frac{\sin \theta}{1+\cos \theta}=2 \csc \theta \) 6. Prove \( \frac{c s c^{2} \theta-1}{c s^{2} \theta}=\cos ^{2} \theta \) 7. Prove \( \frac{1}{1-\cos ^{2}}+\frac{1}{1+\cos \mathrm{B}}=2 \csc ^{2} \) 8. Prove \( \left(\cot ^{2} A+1\right)\left(\sin ^{2} A-1\right)=-\cot ^{2} A \)

c) \( \frac{\sin ^{2} \theta-3 \sin \theta+2}{\sin ^{2} \theta-1}=\frac{\sin \theta-2}{\sin \theta+1} \)

11. Prove the following identities. a) \( \sin \theta \cos \theta \cot \theta=1-\sin ^{2} \theta \)

1. Los ángulos de elevación de un globo desde dos puntos \( A \) y \( B \) al nivel del suelo son \( 24^{\circ} \) y \( 48^{\circ} \), respectivamente. Los puntos \( A \) y están a 4 kilometros entre si, y el globo está entre los puntos, en el mismo plano vertical.