The area of the isosceles triangle is 8 cm 2, and its arm's length is 4 cm. How many percents of the area of the triangle ABC The intersection of the perpendicular and the side AB is point K. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs. Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. What is the height difference that the car went? The road sign which informs the climb is 8.7%-the car drive 5 km along this road. How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm, and Paul is from the tower distance of 20 m. Draw a triangle X'Y'Z' whose base is 8 cm long. The size of the angle at the X vertex is 45 degrees. The base of triangle XYZ has length |XY|=4cm. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tree in meters?Īn observer standing west of the tower sees its top at an altitude angle of 45 degrees. The tree's shadow is three times as long as Miro's shadow. Miro is 180 cm tall, and its shade is 1.5 m long.

Miro stands under a tree and watches its shadow and shadow of the tree. Calculate the height of the house and its distance from the church. Calculate the lighthouse distance from the sįrom the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Marcel lies 15 meters away from the sea (M). Marcel (point J) lies in the grass and sees the top of the tent (point T) and, behind it, the top of the lighthouse (P). Find what part of the ABC triangle contains the trianglĬalculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent to the second leg b, is 5cm.įind all right-angled triangles whose side lengths form an arithmetic sequence. In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. When the man approaches the lighthouse by 90 meters, its shadow is shorter by 3 meters. The male shadow caused by the beacon light is initially 5.4 meters long. Hence, in a right-angled triangle, if we know one other angle, then the ratios of the sides of the triangle are constant.The man, 180 cm tall, walks along the seafront directly to the lighthouse. In a right-angled triangle, we only need to know one other angle and then the angle sum of a triangle gives us the third angle. That is, once the angles of a triangle are fixed, the ratios of the sides of the triangle are constant. Hence the matching angles are the same.įor any right-angled triangle similar to triangle ABC, the ratio of the matching sides will be the same. The triangles pictured are similar (SSS), that is the corresponding sides are in the same ratio. Source: Australian Curriculum, Assessment and Reporting Authority (ACARA) Similarity of right-angled triangles Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223)

Right triangle similarity